Diego Simeone's side shocked Barca with a 2-0 first leg victory at the Nou Camp last week with goals from Julian Alvarez and Alexander Sorloth.
Hansi Flick's team responded at the Metropolitano with early goals from Lamine Yamal (4') and Ferran Torres (24') to level the score, only for a 31st minute Ademola Lookman strike on 31 minutes to settle the tie.
Barca did manage to equalise only for the goal to be ruled out for offsides, while their job was made all that harder in the last ten minutes of the match following the dismissal of Eric Garcia.
Atleti will face the winner of the quarter-final clash between Sporting and Arsenal, while Paris Saint-Germain, who beat Liverpool 4-0 on aggregate, will take on the winner between Real Madrid and Bayern Munich.
Speaking after the game, a delighted Simeone praised his team for some "extraordinary" football.
“We knew about the rival that we were going up against. Extraordinary football, velocity, an attack that's incredible, many means of generating danger. We did commit errors in moments of the game,” he said.
"We couldn't control [everything] and they're very good and it's normal and it was possible that if we didn't control those things we found we would find ourselves in that situation.
"I value this tie, not succumbing to the moment and the errors that we committed for them to score those two goals. We could have avoided that. But that's how it happened. The team got back, worked, and they ran a lot. They ran a lot. An incredible effort.
"It's our fourth Champions League semi-final. It's incredible. The club gives us an opportunity to keep on working with a lot of hope with a lot of enthusiasm with a lot of work and effort and we keep on reinventing ourselves year after year to take Atletico Madrid to the best places in Europe."
Flick added: "Like we always do. We decide what situation we will show them and what we have to make better. We played a fantastic first half. The goal for them was not expected, but it's like football.
"When we see both matches, we deserved to stay in the semi-final. We have to score more goals, but that's life."
"We have to win La Liga. We have to show the attitude mentality. Of course we are disappointed, the fans, players, coaches, for everyone, it's a big dream to win the Champions League.
"We are on that way. We have a young team, and we will improve next season," added the Barca boss.
