The reigning champion, which led 2-1 from the first leg, was beaten 2-0 in Madrid and sent packing 3-2 on aggregate.
Antoine Griezmann scored twice to send Atletico through to the semifinals and end Barcelona's hopes of becoming the first team to retain the Champions League title.
Only once in the past eight seasons had Barcelona failed to reach the semifinal stage of the competition -- that was back in 2014 when it was knocked out in the last eight by Atletico.
No team has ever successfully defended its Champions League title but this year was supposed to be different.
Only a few weeks ago Barcelona was playing football from another planet, it was steamrolling opponents with ease and scoring goals for fun.
There were few who believed Barcelona could be stopped as it embarked on a run of 39 consecutive games without defeat.
But the juggernaut has come to a shuddering halt -- and its main man appears to have gone missing.
Lionel Messi, the diminutive genius, has now failed to score for 452 minutes -- his longest drought since April 2010.
He might even exceed that dry spell if he fails to score within the opening 23 minutes of Sunday's clash with Valencia.
The forward, who has amassed an astonishing 499 career goals, failed to muster a single effort on target in the Champions League for the first time since April 2014 -- a game which was also against Atletico.
It's not just in Europe that Barcelona has had trouble.
Atletico, which was at one stage eight points adrift of La Liga leader Barcelona in Spain's top-flight, has cut the deficit to just three over the past few weeks.
Barcelona's home defeat by Real Madrid in El Clasico and its 1-0 loss at Real Sociedad has cast doubt over its title ambitions.
It has looked tired, unable to muster the kind of form which had made it so irrepressible earlier in the campaign.
And strike it did with a performance which was full of strength, vigor and no shortage of quality.
Atletico had lost its previous seven meetings with Barcelona but this time not only took the bull by the horns -- it was the bull and the horns, rampaging into challenges and chasing its prey across the field.
Led by Diego Simeone, its fierce and feisty coach, Atletico gave a tactical masterclass in how to take on one of the world's best.
Deprived of the suspended Fernando Torres, who followed up his goal in the first leg by picking up two yellow cards, Atletico turned once again to Griezmann.
And it was Atletico's talisman who made the difference as Barcelona were undone by the in-form forward.
Goals for Griezmann
The France striker, who took his tally to 29 for the season, has been one of the outstanding players in European football this season.
Once again, on the big occasion, Griezmann delivered when his team needed it most, heading home Saul's cross nine minutes before the interval.
He then kept his cool from the penalty spot, firing home in the 88th minute after Andres Iniesta had handled the ball.
"The team has made a great effort to be among the best four of Europe," Griezmann told reporters.
"This is a special night for our club. We are very happy with how we played against a very good team in Barcelona."
Atletico captain Gabi hailed his side's performance in a game in which it was forced to defend for long periods and frustrate its opponent.
"The team made a tremendous effort," he said. "We had possession, chances and hit the bar. We qualified fairly, even though in the second half Barcelona forced us back.
"We are in the semifinals, but we have to keep on working with the same humility as always."
Barca second best
Barcelona dominated the contest with 77% of possession but managed just one shot on target in the first half.
It improved after the interval with Luis Suarez -- who scored both Barca goals in the first leg -- forcing Atletico goalkeeper Jan Oblak into a sharp reflex save.
But it wasn't until it went 2-0 down that the visiting side appeared threatening.
Iniesta, who had only just conceded the penalty, struck an effort towards goal which appeared to strike the arm of Gabi.
Barcelona's players protested furiously to the referee, who adjudged the offense to have taken outside of the penalty area, although replays showed this was incorrect.
Messi, who has scored so many memorable goals, stood over the ball but his effort sailed high and wide as the hosts held out.
"It was not to be," Enrique said. " Atletico deserve praise. We really wanted to go further and rise to the challenge (of defending the trophy) but we congratulate Atletico Madrid.
"The first half was really tranquil, they played that way, waiting for us and trying to score a goal against us.
"We have not had our best day, but in the second half we have had chances."
Bayern battles through
Atletico Madrid is joined in the last four by Real Madrid, Manchester City and Bayern Munich, which booked its place in the next round Wednesday.
The German giant was held to a 2-2 draw by Benfica, but progressed 3-2 on aggregate to secure a fifth consecutive semifinal appearance.
Raul Jimenez gave Benfica a 27th-minute lead before Arturo Vidal, who scored in the first game between the teams, leveled on the night.
Thomas Muller then gave the five-time European champion the lead as Bayern took a firm grip on the contest, only for Talisca to equalize 14 minutes from time.
"We played with a big personality," Bayern manager Pep Guardiola told reporters.
"We remained composed and cool in the head even after falling a goal behind. We played very well.
""Every team at this stage is very, very good. But reaching the semifinals for a fifth time in a row is a big thing."