Emmanuel Adebayor's extra-time goal earned Tottenham a place in the Europa League quarter-finals after they held on to knock out a resurgent Inter.
The Italian side overturned a three-goal deficit from the first leg as Antonio Cassano headed in before Rodrigo Palacio's finish and a William Gallas own goal drew the tie level.
But after 96 minutes, Adebayor stabbed in following Mousa Dembele's shot.
Although Ricardo Alvarez made it 4-4 on aggregate, Spurs' away goal was vital.
Adebayor, who scored his fourth goal of the season, made the telling finish for the Premier League side after an otherwise mixed night for the striker, although it was Dembele who was the architect.
Inter Milan scored four goals the last time they played Spurs at the San Siro - winning a Champions League group stage fixture two seasons ago. After taking a 4-0 half-time lead, they held on despite Gareth Bale's second-half hat-trick, winning 4-3.
The Belgium midfielder was Tottenham's saviour in the last round as his injury-time goal earned Spurs
an aggregate victory over Lyon,
and in Milan he broke forward before unleashing a shot that Inter goalkeeper Samir Handanovic could only parry.
Inter had been inches from winning the tie at the end of normal time, but Esteban Cambiasso dragged a shot wide when a goal would have put his side 4-3 in front on aggregate.
Late in extra-time with the tie at 4-4 the Italians pressed for a winner and they will perhaps feel they deserved more after mounting a superb comeback to move to the brink of qualification.
But somehow Spurs sneaked through after a tie where the importance of the suspended Gareth Bale was obvious.
The result was Tottenham's first defeat in the Europa League during their 2012-13 campaign, but Andre Villas-Boas' side became the first English team to reach a European quarter-final this season.
Yet for periods during the game Spurs were outnumbered in midfield and in the first half they paid for committing men forward as gaps opened up behind a reshuffled defence.
Gylfi Sigurdsson filled in for Bale on the left of midfield and provided an early threat for Spurs with some accurate set-pieces but left-back Kyle Naughton was caught out twice by long through-balls down the Inter right before Cassano finally scored.
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Cassano shot straight at Brad Friedel with his first opening and went down theatrically under pressure from Gallas with the second, but he made up for those misdemeanours at the third time of asking on a night where he was at the hub of Inter's best moves.
Again the ball was swept down the right, and this time the Italian striker connected with Palacio's cross at the back post with a downward header.
Six minutes later Inter should have been further in front when Cassano returned the favour with a pass over the top to Palacio, but the Argentine lobbed a shot onto the bar.
Despite their first-leg advantage, Tottenham named Jermain Defoe and Adebayor in attack, and at times, it contributed to their vulnerability.
They still created enough chances in the first half to register a crucial away goal, though, with the best of them falling to Adebayor, who chipped over when clean through. The Togolese then almost set up Jan Vertonghen soon after the re-start as Tottenham continued their positive approach.
Palacio's goal changed that plan after 52 minutes with Cambiasso feeding him for a cool finish past Friedel. Spurs boss Villas-Boas then decided to withdraw Defoe to bolster his midfield in the hope that Spurs could see the game out.
Instead, Javier Zanetti used all his experience to win a free-kick after being pushed by Kyle Walker and when Cassano whipped it in, the ball was diverted into his own goal by the unlucky Gallas.
With the tie now level, Naughton and then Cambiasso almost won it before the extra period. And as the added 30 minutes ensued, Gallas missed a great chance to make amends for his earlier mistake.
Adebayor then finally made his mark on the game, and although Alvarez drew the aggregate scores level, finding another goal proved too much to ask for a shattered Inter.
Centre by Antonio Cassano, Andrea Ranocchia has a header from close range and clears the crossbar.
Short corner taken by Antonio Cassano from the left by-line.
Rodrigo Palacio crosses the ball, William Gallas manages to make a clearance.
Outswinging corner taken right-footed by Antonio Cassano, Headed effort from the edge of the area by Andrea Ranocchia goes wide of the right-hand upright.
The ball is swung over by Rodrigo Palacio, clearance by Scott Parker.
Free kick taken by Guilherme Juan.
Booking Booking for Emmanuel Adebayor for unsporting behaviour.
Unfair challenge on Walter Gargano by Emmanuel Adebayor results in a free kick.
Free kick taken by Lewis Holtby.
Booking Guilherme Juan booked.
Free kick awarded for an unfair challenge on Emmanuel Adebayor by Guilherme Juan.
Free kick awarded for a foul by Walter Gargano on Gylfi Sigurdsson. Direct free kick taken by Lewis Holtby.
Assist on the goal came from Antonio Cassano.
109:07 Goal scored
Goal - Ricardo Alvarez - Int Milan 4 - 1 Tottenham Ricardo Alvarez finds the net with a headed goal from inside the six-yard box. Inter Milan 4 (4)-(4) 1 Tottenham.
The ball is swung over by Antonio Cassano,
Free kick awarded for a foul by Ricardo Alvarez on Jan Vertonghen. Free kick taken by William Gallas.
Substitution Andrea Ranocchia is brought on as a substitute for Moreira Jonathan.
Corner taken by Ricardo Alvarez from the right by-line played to the near post, clearance made by Emmanuel Adebayor.
Effort from 25 yards by Antonio Cassano. Brilliant save by Brad Friedel.
Second half of extra-time has started.
Rodrigo Palacio produces a cross, clearance made by William Gallas.
Effort from 12 yards by Rodrigo Palacio. Save made by Brad Friedel. Short corner taken by Rodrigo Palacio from the right by-line. Shot by Moreira Jonathan from 18 yards. Save by Brad Friedel.
The ball is crossed by Guilherme Juan, save by Brad Friedel.
Corner taken by Antonio Cassano.
Substitution Steven Caulker joins the action as a substitute, replacing Kyle Naughton.
Unfair challenge on Scott Parker by Esteban Cambiasso results in a free kick. Kyle Walker takes the direct free kick.
The referee blows for offside against Walter Gargano. Free kick taken by Brad Friedel.
95:57 Goal scored
Goal - Emmanuel Adebayor - Int Milan 3 - 1 Tottenham Emmanuel Adebayor gets on the score sheet with a goal from close range low into the middle of the goal. Inter Milan 3 (3)-(4) 1 Tottenham.
Effort from 20 yards by Mousa Dembele. Save made by Samir Handanovic.
Foul by Moreira Jonathan on Gylfi Sigurdsson, free kick awarded. Free kick taken by Lewis Holtby.
Corner taken by Gylfi Sigurdsson from the right by-line, Header from close range by William Gallas misses to the right of the goal.
Corner from the left by-line taken by Gylfi Sigurdsson, Esteban Cambiasso makes a clearance.
Aaron Lennon takes a shot. Javier Zanetti gets a block in.
The whistle goes to signal the end of normal time, with extra time looming.
The official flags Lewis Holtby offside.
Effort on goal by Esteban Cambiasso from inside the box misses to the right of the target.
Shot by Rodrigo Palacio from just outside the area goes over the net.
Ricardo Alvarez takes a shot. Brad Friedel makes a save.
Outswinging corner taken right-footed by Gylfi Sigurdsson, Rodrigo Palacio manages to make a clearance.
Shot by Kyle Naughton. Save made by Samir Handanovic.
Ricardo Alvarez takes the outswinging corner, Guilherme Juan takes a shot. Save made by Brad Friedel.
The ball is swung over by Rodrigo Palacio, Kyle Naughton makes a clearance.
William Gallas gives away a free kick for an unfair challenge on Antonio Cassano. Free kick taken by Marco Benassi.
Substitution Marco Benassi comes on in place of Mateo Kovacic.
Booking Lewis Holtby is shown a yellow card.
The referee blows for offside. Indirect free kick taken by Guilherme Juan.
Corner taken by Antonio Cassano, William Gallas makes a clearance.
The ball is sent over by Antonio Cassano, blocked by Lewis Holtby.
Booking Lewis Holtby is booked.
Free kick taken by Guilherme Juan.
Substitution Marco Benassi joins the action as a substitute, replacing Mateo Kovacic.
Booking Kyle Walker is cautioned by the ref for unsporting behaviour.
Guilherme Juan fouled by Kyle Walker, the ref awards a free kick.
74:58 Goal scored
Goal - William Gallas - Int Milan 3 - 0 Tottenham William Gallas puts the ball into his own goal from 6 yards. Inter Milan 3 (3)-(3) 0 Tottenham.
Unfair challenge on Javier Zanetti by Kyle Walker results in a free kick. Shot on goal comes in from Antonio Cassano from the free kick.
The ball is delivered by Lewis Holtby, clearance made by Cristian Chivu.
The referee blows for offside against Rodrigo Palacio. Free kick taken by Brad Friedel.
Substitution (Inter Milan) makes a substitution, with Ricardo Alvarez coming on for Fredy Guarin.
Jan Vertonghen restarts play with the free kick.
Substitution Aaron Lennon replaces Jake Livermore.
Gylfi Sigurdsson fouled by Moreira Jonathan, the ref awards a free kick.
Javier Zanetti takes a shot. Save by Brad Friedel.
The ball is delivered by Moreira Jonathan.
The offside flag is raised against Emmanuel Adebayor. Guilherme Juan takes the indirect free kick.
Antonio Cassano is flagged offside by the assistant referee. Indirect free kick taken by Brad Friedel.
Emmanuel Adebayor gives away a free kick for an unfair challenge on Cristian Chivu. Free kick taken by Mateo Kovacic.
Rodrigo Palacio delivers the ball, Brad Friedel makes a save.
The assistant referee flags for offside against Emmanuel Adebayor. Cristian Chivu takes the indirect free kick.
Jan Vertonghen gives away a free kick for an unfair challenge on Rodrigo Palacio. Centre by Antonio Cassano, Headed effort from deep inside the penalty area by Esteban Cambiasso goes harmlessly over the crossbar.
Lewis Holtby concedes a free kick for a foul on Fredy Guarin. Free kick taken by Fredy Guarin.
Walter Gargano gives away a free kick for an unfair challenge on Scott Parker. Free kick taken by Kyle Naughton.
Direct free kick taken by Kyle Naughton.
Substitution Jermain Defoe goes off and Lewis Holtby comes on.
Free kick awarded for an unfair challenge on Scott Parker by Walter Gargano.
Assist by Esteban Cambiasso.
51:37 Goal scored
Goal - Rodrigo Palacio - Int Milan 2 - 0 Tottenham Rodrigo Palacio fires in a goal from inside the penalty area to the bottom right corner of the goal. Inter Milan 2 (2)-(3) 0 Tottenham.
Jan Vertonghen has an effort at goal from 12 yards.
Emmanuel Adebayor is penalised for handball and concedes a free kick. Free kick taken by Guilherme Juan.
Free kick awarded for an unfair challenge on Jan Vertonghen by Fredy Guarin. William Gallas restarts play with the free kick.
The assistant referee signals for offside against Rodrigo Palacio. William Gallas takes the indirect free kick.
The game restarts for the second half.
45:00 +2:22 Half time
Half Time The referee calls an end to the first half.
Emmanuel Adebayor produces a left-footed shot from inside the area that clears the crossbar.
Fredy Guarin gives away a free kick for an unfair challenge on William Gallas. Brad Friedel restarts play with the free kick.
Fredy Guarin takes a shot. Brilliant save by Brad Friedel.
Handball decision goes against Emmanuel Adebayor. Cristian Chivu takes the free kick.
Rodrigo Palacio crosses the ball.
Booking Brad Friedel goes into the referee's book for time wasting.
Shot by Fredy Guarin from outside the box goes high over the target.
Inswinging corner taken right-footed by Gylfi Sigurdsson from the left by-line, Samir Handanovic makes a brilliant save.
Scott Parker gives away a free kick for an unfair challenge on Mateo Kovacic. Guilherme Juan restarts play with the free kick.
Rodrigo Palacio gives away a free kick for an unfair challenge on Kyle Naughton. Brad Friedel takes the direct free kick.
Unfair challenge on Mousa Dembele by Esteban Cambiasso results in a free kick. Gylfi Sigurdsson crosses the ball, Headed effort from deep inside the penalty area by Kyle Walker misses to the left of the goal.
Jermain Defoe crosses the ball, clearance by Guilherme Juan.
Moreira Jonathan is ruled offside. Free kick taken by Brad Friedel.
Rodrigo Palacio is flagged offside by the assistant referee. Jan Vertonghen restarts play with the free kick.
Antonio Cassano takes the chance to get an effort at goal. Save made by Brad Friedel.
Rodrigo Palacio takes a shot.
Shot on goal by Emmanuel Adebayor from just inside the area clears the crossbar.
Emmanuel Adebayor is caught offside. Free kick taken by Walter Gargano.
Esteban Cambiasso takes the chance to get an effort at goal. Comfortable save by Brad Friedel.
Antonio Cassano fouled by Jake Livermore, the ref awards a free kick. Walter Gargano takes the direct free kick.
Shot by Gylfi Sigurdsson. Save made by Samir Handanovic.
The offside flag is raised against Antonio Cassano. Indirect free kick taken by William Gallas.
Assist by Rodrigo Palacio.
19:06 Goal scored
Goal - Antonio Cassano - Int Milan 1 - 0 Tottenham Antonio Cassano finds the net with a headed goal from close in. Inter Milan 1 (1)-(3) 0 Tottenham.
Esteban Cambiasso fouled by Kyle Walker, the ref awards a free kick. Free kick taken by Esteban Cambiasso.
The official flags Jermain Defoe offside. Guilherme Juan takes the free kick.
Direct free kick taken by Jan Vertonghen.
Booking Jake Livermore booked for time wasting.
Free kick awarded for an unfair challenge on Scott Parker by Esteban Cambiasso.
Effort on goal by Antonio Cassano from 18 yards. Save made by Brad Friedel.
Gylfi Sigurdsson delivers the ball.
Corner taken right-footed by Gylfi Sigurdsson from the right by-line, clearance made by Rodrigo Palacio.
Jermain Defoe has an effort at goal from 20 yards. Blocked by Guilherme Juan.
Antonio Cassano is caught offside. Jan Vertonghen restarts play with the free kick.
Free kick awarded for a foul by Guilherme Juan on Kyle Naughton. Kyle Naughton takes the free kick.
Gylfi Sigurdsson fouled by Guilherme Juan, the ref awards a free kick. Free kick crossed right-footed by Gylfi Sigurdsson from left wing, clearance made by Cristian Chivu.
The game begins.
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