Match ends, Atlético de Madrid 2, Barcelona 0.
Holders Barcelona suffered a shock Champions League exit as Antoine Griezmann's double sent Atletico Madrid into the semi-finals.
Barca arrived in Spain's capital with a 2-1 advantage from the first leg but poor defending allowed the unmarked Griezmann to power home Saul's cross.
Saul headed against the bar as Barca toiled before Griezmann scored a late penalty after Andres Iniesta handled.
Barca were denied a penalty when Gabi handled just inside the area.
The defeat ended Luis Enrique's hopes of securing a La Liga, Champions League and Copa del Rey treble, while Atletico join Bayern Munich, Manchester City and Real Madrid in Friday's semi-final draw (11:30 BST).
Barcelona's players surrounded the referee after Gabi clearly handled inside the area though he was standing outside it, the referee awarding only a free-kick.
Listen again:'Simeone is the archetypal baddie'
But Barca were a shadow of the team that conquered Europe so convincingly last season and have now lost three of the last four games in all competitions.
In addition, Lionel Messi failed to score for the fifth game in a row for his club, and Neymar and Luis Suarez were frustrated by excellent home defending.
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On the rare occasions Suarez managed to work an opening he found Jan Oblak in fine form on a great night for Atletico.
Barca's bad-tempered exit
The tie was littered with late challenges - there were eight bookings in total - while there were two flashpoints as Barca exited the competition on a bad-tempered note.
Suarez caught Uruguay team-mate Diego Godin with an elbow that left the Atletico defender with a swelling above his eye.
And another scuffle between the top two clubs in Spain broke out when Neymar appeared to lash out at Juanfran from behind.
Barca enjoyed 77% possession and had more shots than Atletico , yet could not disguise their frustration as they were undone by Griezmann's double.
History repeats itself
This was the eighth meeting in 15 months between the sides, with Barcelona having won the previous seven.
Indeed, Atletico's most recent win over their oppoents was at this stage of the Champions League two years ago.
Barcelona suffered a 2-1 aggregate defeat in 2014 with Diego Simeone's side eventually reaching the final - only to lose 4-1 to Real Madrid after extra time.
Simeone will be confident after this fine performance that his side can go one better this time.
Wait goes on for Messi
Messi remains on 499 career goals, just as he has done since 30 March when he scored for Argentina.
He has gone 452 minutes without scoring for Barcelona.
On Wednesday, Messi did not look like finding the net as he failed to register a shot on target in a Champions League game for the first time since 2014 - also against Atletico.
The 28-year-old cut a frustrated figure as Godin and Lucas Hernandez produced commanding performances at the heart of the home defence.
Messi's last touch of the game was a free-kick on the edge of the area, when they should have had a penalty, which flew wide.
It summed up Barcelona's night.
Man of the Match - Diego Godin (Atletico Madrid)
The stats you need to know
- No team has still ever retained the Champions League since its inception in 1992/93.
- Only Diego Costa in 2013/14 (8 goals) has scored more for Atletico Madrid in a Champions League season than Antoine Griezmann has for them this campaign (6).
- It was Griezmann's third Champions League brace this season, after scoring two in both matches against Galatasaray
- Barcelona failed to score in a Champions League game for the first time since April 2014, which was also against Atletico Madrid.
Barcelona are three points clear at the top of La Liga with six games remaining. They will look to put this result behind them when they entertain Valencia on Sunday (19:30 BST)
Atletico host Granada on the same day at 17:15 BST.
- 20Torres Belén
- 2GodínBooked at 85mins
- 3Filipe Luís
- 14Fernández ArenasBooked at 68mins
- 12FernándezSubstituted forSavicat 90+3'minutes
- 6KokeBooked at 90mins
- 7GriezmannSubstituted forCorreaat 90'minutesBooked at 90mins
- 21CarrascoSubstituted forParteyat 74'minutes
- 1Moyá Rumbo
- 1ter Stegen
- 6Alves da SilvaSubstituted forRoberto Carnicerat 64'minutes
- 4RakiticSubstituted forTuranat 64'minutesBooked at 90mins
- 8IniestaBooked at 87mins
- 9SuárezBooked at 70mins
- 11NeymarBooked at 76mins
- 2Pereira dos Santos
- 17El Haddadi
- 20Roberto Carnicer
- Nicola Rizzoli
- Shots on Target
Second Half ends, Atlético de Madrid 2, Barcelona 0.
Koke (Atlético de Madrid) is shown the yellow card.
Neymar (Barcelona) wins a free kick in the defensive half.
Foul by Juanfran (Atlético de Madrid).
Substitution, Atlético de Madrid. Stefan Savic replaces Augusto Fernández.
Attempt missed. Lionel Messi (Barcelona) left footed shot from outside the box is just a bit too high from a direct free kick.
Arda Turan (Barcelona) is shown the yellow card.
Hand ball by Gabi (Atlético de Madrid).
Ángel Correa (Atlético de Madrid) is shown the yellow card.
Substitution, Atlético de Madrid. Ángel Correa replaces Antoine Griezmann.
Arda Turan (Barcelona) wins a free kick in the attacking half.
Foul by Antoine Griezmann (Atlético de Madrid).
Goal! Atlético de Madrid 2, Barcelona 0. Antoine Griezmann (Atlético de Madrid) converts the penalty with a left footed shot to the bottom right corner.
Andrés Iniesta (Barcelona) is shown the yellow card for hand ball.
Penalty conceded by Andrés Iniesta (Barcelona) with a hand ball in the penalty area.
Diego Godín (Atlético de Madrid) is shown the yellow card for a bad foul.
Sergi Roberto (Barcelona) wins a free kick on the right wing.
Foul by Diego Godín (Atlético de Madrid).
Javier Mascherano (Barcelona) wins a free kick on the left wing.