Match ends, Wolverhampton Wanderers 1, Tottenham Hotspur 2.
Tottenham manager Jose Mourinho said his side had won an "incredible three points" against a Wolves team he believes can challenge for the Champions League places.
Jan Vertonghen scored a dramatic late winner as Spurs ended Wolves' 11-match unbeaten Premier League run to narrow the gap on the top four with victory at Molineux.
Vertonghen headed in from a corner in injury time, after Wolves' relentless approach had been rewarded as Adama Traore thumped in a deserved equaliser from the edge of the box midway through the second half.
On Wolves, Mourinho said: "My feeling is they are fighting for more than they said. They are not just there for the top six. They can do more. They are a fantastic team. This is a big victory.
"This game is a special game because the opponent is a special opponent. Nuno [Espirito Santo] has to be very proud of Wolves' record."
On his own side's progress, he added: "We went about a year without winning a Premier League game away and we've managed two in a short amount of time. Now we are not looking to the bottom of the table, we're looking higher up."
Following a breathless opening period, Lucas Moura's mazy run and exquisite finish into the roof of the net had put Tottenham ahead after eight minutes.
Spurs had to withstand intense pressure as Wolves chased an equaliser, but it was they who went closest before half-time as Eric Dier struck the post from Dele Alli's delightful, dinked pass.
Tottenham goalkeeper Paulo Gazzaniga produced an excellent save from Romain Saiss' header in the closing stages as Mourinho's visitors appeared to be hanging on, before Vertonghen's decisive goal.
Victory sees Tottenham climb above Wolves to fifth, three points behind fourth-placed Chelsea who they face next Sunday (16:30 GMT).
Spurs weather storm to close in on top four
Ahead of his side's trip to Molineux, Tottenham boss Mourinho made clear his belief that Spurs will qualify for next season's Champions League via a top-four finish in the Premier League.
Vertonghen's late header has suddenly turned that into a very realistic prospect, with Spurs set to welcome the Blues - who slumped to a fourth league defeat in five against Bournemouth on Saturday - to Tottenham Hotspur Stadium next weekend.
Aiming for a fifth consecutive top-four finish, Spurs have narrowed an 11-point gap to the Champions League places with four wins from five league games since Mourinho's appointment.
With the top-four door ajar, Spurs made a purposeful start as Son Heung-min saw an attempt stopped by Rui Patricio, but it did not take long for their early enthusiasm to pay off as Moura's fast feet and emphatic finish stunned Wolves.
A second goal always appeared crucial for Mourinho's side, who had conceded at least two goals in five of their six games under the Portuguese prior to kick-off, as the energetic hosts dominated in possession and territory.
Often unconvincing, the Spurs backline weathered the storm and allowed for counter opportunities - but Dier was unable to provide the finish that Alli's sublime pass over the Wolves defence deserved.
Outplayed and having not kept a clean sheet away from home since New Year's Day - a club-record run of 16 matches - Traore's equaliser came as no surprise.
What will delight Mourinho, however, was the determined manner of his side's response to conceding, and a confidence-boosting late winner that puts their top-four hopes firmly in their own hands.
Result harsh on impressive Wolves
As the halfway stage of the season approaches, a Wolves side which could be forgiven for suffering a hint of fatigue played with an intensity and determination that was fully deserving of a point - if not all three.
Nuno Espirito Santo has praised his players' commitment and togetherness during their packed campaign, which has seen them play 31 games as they juggle domestic competition with their first European campaign in almost 40 years.
Wolves typically relish their match-ups with the Premier League's big sides and responded to their early setback in style with a swashbuckling home display.
The ever-improving Traore's low drive forced Gazzaniga into action, while Raul Jimenez dragged wide and Diogo Jota saw an attempt blocked following a swift counter as the hosts began to pick their way through the Tottenham defence.
Despite contesting their fifth game in 15 days, Wolves pressed and harried Spurs, boasting 87.5% of possession in the final five minutes of the first half, but to no avail.
They emerged in the second half with the same intent, as Joao Moutinho and Ruben Neves continued to dictate the play and Jimenez again went close before Traore's spectacular equaliser after 67 minutes.
A menace all game, Toby Alderweireld and Vertonghen struggled to cope with Traore's frightening pace down the right, with Spurs resorting to fouling the 23-year-old as he threatened to burst away on several occasions.
With a point on the horizon, conceding in the 91st minute will come as a huge disappointment to Nuno's side - though once the dust settles they will surely feel proud of another excellent showing.
Man of the match - Adama Traore (Wolves)
'Three incredible points' - what they said
Tottenham manager Jose Mourinho: "We knew the game was going to be difficult. They didn't catch us by surprise. We had a very good start like we tried to. We almost scored a second goal but against Wolves that would not have killed the game.
"We knew if we arrive in the last part we could score. After that we had to close the door for the last five minutes. Three incredible points."
Wolves manager Nuno Espirito Santo: "Of course I'm pleased with the performance. We played very good. We weren't perfect, almost. We should have defended better. We played well and created chances. I'm very pleased with the boys.
"The final moments require a lot of focus. We must stay in the game until the end. We were more obsessed about scoring than defending."
Last-gasp winners a rarity for Spurs - the stats
- Tottenham have won two of their three Premier League away games under Jose Mourinho, as many as they did in Mauricio Pochettino's final 14 away from home in the competition.
- Since a 3-1 defeat as Chelsea boss in October 2015, Mourinho has not lost any of his last 54 Premier League games when his side has scored the opening goal.
- Lucas Moura has scored three goals in five Premier League appearances under Mourinho after managing only one in 10 games under Pochettino earlier this season.
- Jan Vertonghen scored Tottenham's first 90th-minute winner in the Premier League since Harry Winks against Fulham in January.
- Wolves suffered just their third home defeat in the top flight in 2019 and their first since a 5-2 defeat by Chelsea in September.
- Adama Traore's equaliser for Wolves was his fourth goal of the season in 26 appearances, which is twice as many as he scored in his previous 82 matches as a Premier League player in all competitions.
- No two players have combined for more Premier League goals this season than Traore and Raul Jimenez.
Tottenham will learn their Champions League last-16 opponents in Monday's draw, with Barcelona, Juventus, Paris St-Germain, Valencia and RB Leipzig possible opponents.
They will then have their shot at leapfrogging current fourth-placed Chelsea on Sunday (16:30 GMT).
The likes of Ajax, Inter Milan and Sevilla are potential opponents for Wolves in the Europa League last-32 draw, with a trip to Norwich to come on Saturday (15:00).
- 11Rui Patrício
- 32DendonckerBooked at 89mins
- 27SaïssBooked at 75mins
- 28João MoutinhoBooked at 60mins
- 19Castro OttoBooked at 65mins
- 6D SánchezBooked at 64mins
- 4AlderweireldBooked at 69mins
- 15DierBooked at 77mins
- 27Lucas MouraSubstituted forEriksenat 89'minutes
- 20AlliSubstituted forWinksat 90+2'minutes
- 7Son Heung-MinSubstituted forFoythat 90+2'minutes
- 10KaneBooked at 83mins
- 18Lo Celso
- 19R Sessegnon
- Stuart Attwell
- Shots on Target
Second Half ends, Wolverhampton Wanderers 1, Tottenham Hotspur 2.
Attempt missed. Diogo Jota (Wolverhampton Wanderers) right footed shot from outside the box is close, but misses to the right.
Attempt blocked. Rúben Neves (Wolverhampton Wanderers) right footed shot from outside the box is blocked. Assisted by Romain Saïss.
Corner, Wolverhampton Wanderers. Conceded by Toby Alderweireld.
Substitution, Tottenham Hotspur. Juan Foyth replaces Son Heung-Min.
Substitution, Tottenham Hotspur. Harry Winks replaces Dele Alli.
Goal! Wolverhampton Wanderers 1, Tottenham Hotspur 2. Jan Vertonghen (Tottenham Hotspur) header from the centre of the box to the bottom left corner. Assisted by Christian Eriksen with a cross following a corner.
Corner, Tottenham Hotspur. Conceded by Raúl Jiménez.
Substitution, Tottenham Hotspur. Christian Eriksen replaces Lucas Moura.
Leander Dendoncker (Wolverhampton Wanderers) is shown the yellow card for a bad foul.
Foul by Leander Dendoncker (Wolverhampton Wanderers).
Harry Kane (Tottenham Hotspur) wins a free kick on the left wing.
Hand ball by Diogo Jota (Wolverhampton Wanderers).
Jonny (Wolverhampton Wanderers) wins a free kick on the left wing.
Foul by Serge Aurier (Tottenham Hotspur).
Attempt missed. Diogo Jota (Wolverhampton Wanderers) left footed shot from a difficult angle on the left is too high following a set piece situation.
Attempt saved. Romain Saïss (Wolverhampton Wanderers) header from the right side of the box is saved in the bottom left corner. Assisted by João Moutinho with a cross.
Harry Kane (Tottenham Hotspur) is shown the yellow card for a bad foul.
Adama Traoré (Wolverhampton Wanderers) wins a free kick on the right wing.