Cristiano Ronaldo scored two early goals, but the Portuguese missed his spot-kick as Bayern came through the semi-final on penalties.
Madrid: Bayern Munich beat Real Madrid 3-1 on penalties on Wednesday to secure their place against Chelsea in the Champions League final following a memorable contest between the long-time European rivals.
Cristiano Ronaldo looked to have put the home side on their way to the final with two early goals, but just like their Spanish rivals Barcelona the evening before, Madrid faltered. Hungarian referee Victor Kassai awarded Bayern a penalty kick after Pepe pushed Mario Gomez, and Arjen Robben's 27th-minute penalty levelled the score over two legs at 3-3 and also evened the away goals 1-1.
The score stayed that way through the second half and 30 minutes of extra-time, forcing the shoot-out, the first in the semi-finals since Liverpool defeated Chelsea in 2007.
"Trailing 2-0, everyone knows the atmosphere here, everyone knows how difficult it is to come back from this score. But we improved with each minute and played organized in defense," said Heynckes, who was Madrid's coach when it won the 1998 European Cup, as the Champions League was known then.
In the shoot-out, Manuel Neuer saved from Ronaldo and Kaka to put Bayern on course after they had scored their opening two kicks, but counterpart Iker Casillas denied Toni Kroos and Philipp Lahm to drag Madrid back into it.
After Xabi Alonso scored Madrid's first, Sergio Ramos sent his shot high over the bar and Bastian Schweinsteiger sent his effort straight down the middle to ensure Bayern will become the first team to play the final on their home ground. The final is on May 19 at the Allianz Arena.
"When I think about the fact that we can play a final in our own stadium, this is something to go absolutely crazy about," Bayern coach Jupp Heynckes said.
Go wild Bayern and their fans did, Bastian Schweinsteiger ripping his shirt off and going screaming toward the Bayern fans, who stayed on the field long after Madrid coach Jose Mourinho — who watched the shoot-out on his knees — descended into the tunnel. Madrid's players left the field with their heads hanging low, and some were in tears after coming so close to reaching their first final in 10 years.
"It's a big blow for us. It was a very exciting game, but penalties are always a lottery," Madrid goalkeeper Iker Casillas said. "We played well, but Bayern are a great team. We now have to concentrate on the league."
Bayern, four-time champions of European soccer's top club tournament, reached the final for the second time in three seasons.
"We will be very much at home in our own stadium and will be in front of a majority of German supporters, but it won't be easy," Heynckes said. "Today we proved we are a great team. We showed today we play very well at football."
Defending champions Barcelona were knocked out by underdogs Chelsea on Tuesday despite the London side being down to 10 men for most of the match. Barca star Lionel Messi missed a penalty early in the second half and left the Camp Nou pitch in tears.
Madrid's 2-1 win over Barcelona at the weekend gave Jose Mourinho's side a seven-point lead in the league with four games remaining, but their wait for a first Champions League title since 2002 goes on.
Following Bayern's 2-1 win in Germany last week, the 20th meeting between Madrid and Bayern maintained a relentless pace in the first half. Madrid charged out into an early lead after David Alaba handled when sliding to block Angel Di Maria's cross. Ronaldo showed no jitters as he stepped up to drill the spot-kick into the right of goal with goalkeeper Neuer guessing left.
Bayern could easily have cancelled out Ronaldo's opener minutes later as Robben shot over with only Casillas to beat.
Ronaldo's 10th goal of the tournament made it 2-0 in the 14th following an excellent build-up that saw the Spanish leaders spread the ball around with Sami Khedira finding Mesut Oezil, who spotted a wide open Ronaldo outside the area to coolly pick his spot low and to the left.
"The first 15 minutes didn't go as we hoped to," said Heynckes, who led Madrid to victory in the competition in 1998. "Trailing 2-0, everyone knows the atmosphere here, everyone knows how difficult it is to come back from this score. But we improved with each minute and played organized in defence."
While Madrid thrived off the break, Bayern's reliance on possession and wingers Franck Ribery and Robben finally paid off in the 26th when Pepe was late to cover Mario Gomez, the Portugal centreback booked for bundling the Germany striker down as they chased a ball into the area. Casillas guessed right and got a touch but could not keep Robben's powerful spot-kick out.
Ronaldo and Karim Benzema continued to create problems for Bayern as Benzema curled around the far post after the half-hour mark, while Neuer denied Ronaldo from long-range. Casillas saved from Gomez moments later before capping an electric first half by diving to push Robben's free kick from just outside the area wide.
The European heavyweights kept pushing forward in the second half but, with the stakes rising, neither wanted to expose themselves and the chances dwindled, with Gomez heading wide before Neuer pushed Benzema's shot out in the 56th.
Ronaldo couldn't muster up much either as he tamely sent several free kicks straight at Neuer. Gomez wasted a golden opportunity for Bayern when he delayed his shot too long in the 86th, allowing Sergio Ramos and Khedira to smother the chance.
The tempo dipped dramatically in extra-time, when Thomas Mueller replaced Ribery and Gonzalo Higuain came on for Benzema. Madrid conjured up a few more opportunities than their opponents, with substitute Kaka misplaying a fine chance in the 112th.
In the shoot-out, Alaba beat Casillas with the first kick, and Neuer saved Ronaldo's shot. Coming in, Ronaldo had converted 26 of 27 penalty kicks for Real Madrid. The only time he failed was when Almeria's Diego Alves saved him in a Spanish league match on December 5, 2009, his first season in Madrid. Ronaldo also had a penalty saved by Chelsea's Petr Cech in the 2008 Champions League final.
Gomez converted his kick for a 2-0 lead, and Neuer stopped Kaka's shot. Casillas then denied Toni Kroos, Xabi Alonso scored for Madrid, and Casillas stopped Philipp Lahm.
Ramos sent his shot high over the bar — as if it were an NFL field goal — and Schweinsteiger put his shot straight down the middle as Casillas dived left, giving Bayern their fourth victory in five semi-final meetings with Madrid.
"It's so unique to reach the final in Madrid, who are just about Spanish champions over Barcelona," Heynckes said. "This makes me very proud to have made it to the final."
Madrid and Barcelona were considered by many to be Europe's top two teams this year. Ronaldo has scored a Spanish league-record 42 goals, with Lionel Messi one behind him. But neither will be playing in the finale for Europe's top-tier competition.
It is the second straight year that Madrid bowed out in the semi-finals. Real, in their second season under coach Jose Mourinho, have not reached the final since winning in 2002.
Mourinho said Madrid were at something of a disadvantage because they couldn't rest players last weekend like Bayern did. While the Bundesliga league race was wrapped up, Madrid had to face Barcelona in a game that essentially decided the Spanish league title. Still, Mourinho conceded that Bayern "deserve to go through."
"When it got to 2-1, it became difficult to play, the players knew they couldn't make any mistakes," he said.
"That's the beauty of football, nobody knows what's going to happen," Mourinho said. "I hope it's a good final."