A goal from Antoine Griezmann sent Atletico Madrid to the Champions League final for the second time in three seasons despite a 2-1 defeat at Bayern Munich on Tuesday.
Atletico, which lost to city rival Real Madrid in the 2014 final, progressed on the away goals rule with an aggregate score of 2-2 after winning the first leg of their semifinal in Madrid 1-0.
Atletico striker Fernando Torres had the chance to settle it with a late penalty, only for Manuel Neuer to save his spot kick.
Torres wasn't the only one to miss from the spot. Atletico's Jan Oblak saved a penalty from Thomas Mueller in the first half, minutes after Xabi Alonso leveled the tie with a free kick in the 31st.
Griezmann scored in the 54th to put Atletico in the driving seat, before Robert Lewandowski headed Bayern back in front on the night in the 74th to set up a furious finale.
Bayern needed one more goal to avoid going out at the semifinal stage for the third straight season to a Spanish team and poured everything forward — only to be denied by Oblak and his defenders.
"We're into the final. We can be proud and happy. Bayern have amazing players up front and it was impossible to keep a clean sheet," Oblak said.
Atletico will play either Manchester City or Real Madrid in the final in Milan on May 28. Their first leg match finished 0-0 last week in Manchester, with the return match in Madrid on Wednesday.
Atletico coach Diego Simeone described Bayern as "the best team that I played against in my career. It's great to see how my team played with such intensity. I was literally in love with this game."
Simeone, whose side defeated Barcelona in the quarterfinals, added: "We have played against two of the three best teams in Europe. We've knocked them out, and I'm very proud of that."
Torres had no preference over another Madrid derby or an Anglo-Spanish final in Milan.
"We have the chance to create history," he said. "We want to win the tournament and the opponent is irrelevant."
Bayern started Tuesday's game with the intensity needed to claw back the deficit from the first leg.
Lewandowski epitomized the home side's spirit by fighting for every ball, earning a corner at one stage when it looked like a lost cause.
Lewandowski, being marshaled by Diego Godin, was inches away from meeting Douglas Costa's cross and Arturo Vidal fired the next opportunity over the top as Bayern kept up the pressure.
Gabi drew a fine save from Neuer in what was Atletico's best first-half chance after Griezmann pulled the ball back.
After that, it was all Bayern, which had 35 attempts on goal compared to Atletico's seven over the course of the game.
Mueller and Lewandowski both went close and Vidal had another effort stopped by Oblak, who pulled off a brilliant save to deny Lewandowski in the 20th minute when it seemed the Poland striker must score.
Atletico was living dangerously and Simeone was getting increasingly agitated on the touchline. Oblak was relieved to see the ball fly over after a goalmouth fumble and the Atletico goalkeeper was warned for time wasting with less than half an hour played.
A blatant foul from Augusto Fernandez gave Bayern the free kick from which Alonso scored with the help of a deflection from Jose Maria Gimenez.
Gimenez was then penalized for a push on Javi Martinez but Mueller was thwarted from the resultant penalty by Oblak, who also blocked Alonso's effort from the rebound.
"Sometimes football is cruel. Of course I'm really disappointed that I couldn't put it away," Mueller said.
Griezmann scored the decisive goal after combining with Torres, heading the ball to his teammate and then racing onto the return pass to finish coolly past Neuer on a breakaway.
"We were punished by the counterattack. We tried everything. Unfortunately it wasn't enough. It's bitter that we go out after such a game," Bayern captain Philipp Lahm said.
Bayern kept trying, forcing Godin and Gimenez into clearances, and Oblak to make a number of saves before Lewandowski finally made a breakthrough, heading home from close range after Vidal sent a header across goal from David Alaba's cross.
It was as good as it got for Bayern and means coach Pep Guardiola's dream of a treble from his last season in charge is over. The Spanish coach is joining Manchester City next season.
"It's a pity that we couldn't reward ourselves and the coach for the last three years," Lahm said.
Guardiola was asked if his latest Champions League exit meant that his three-year mission at Bayern wasn't fulfilled.
"Perhaps," he replied. "I was very happy here. It was my ambition to win the Champions League here. My job is to help the players play as well as possible and to win as much as possible. I did my best, I've no regrets."
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