Mario Mandzukic, Thomas Mueller and Arjen Robben scored second-half goals for a 3-1 victory Wednesday night that advanced the defending champions to the Champions League semifinals for the third straight year.
"I think it was very important we scored straight after they did," Robben said after the 4-2 aggregate win. "It was crucial today. It looked like a wake-up call because the first 10 minutes of the second half were a disaster the way we played. We were so slow. We were not there, and you cannot do that in the Champions League — you will be punished."
In the night's other game, Koke's fifth-minute goal on a header off Adrian's headed pass led Atletico Madrid over visiting Barcelona 1-0 for a 2-1 aggregate win. Chelsea and Real Madrid advanced earlier in the week to the semifinal draw on Friday.
Following a 1-1 tie at Old Trafford last week in the first leg, Manchester United went ahead when Patrice Evra scored on a left-footed volley from the edge of the penalty area in the 57th minute.
Mandzukic tied the score two minutes later with a diving header off Franck Ribery's cross, beating goalkeeper David de Gea. Mueller put Bayern ahead in the 68th when he knocked in Robben's low cross, and Robben got the final goal in the 76th with a shot that deflected off a foot of defender Nemanja Vidic.
"I had no time to tell my players anything or to think what we could do after we conceded that amazing goal," Bayern coach Pep Guardiola said. "I am very proud of my team and of this club. ... They have a big heart and reacted very well. As title holders, we have a lot of pressure."
Manchester United's elimination assures a trophy-less first season for manager David Moyes, who replaced Alex Ferguson after last season. Knocked out of the FA Cup and League Cup, United is seventh in the Premier League with five games remaining, 17 points behind first-place Liverpool.
United also is seven points behind fourth-place Arsenal in the Premier League and is likely to miss qualifying for the Champions League for the first time since 1995-96.
"I thought the players did a great job today," Moyes said. "We made it difficult for them for long periods but at the end we just couldn't keep it."
Wayne Rooney, who had not trained this week because of a toe injury, played after receiving an injection and sent a shot wide in the 62nd with only goalkeeper Manuel Neuer to beat.
"We had a great chance to go to 2-2," Moyes said. "Munich are a very good team and we had to defend very well. I am disappointed we didn't take those chances."
Atletico, which leads Barcelona by one point in the Spanish league, reached the last four of Europe's top club competition for the first time since 1974. Barcelona had reached the semifinals for six straight years.
"There was a big difference between one team and another early on. We couldn't string together four or five passes like we needed to," Barcelona coach Gerardo Martino said. "If we had managed to equalize we might have been able to play the game we wanted."
Atletico and Barcelona had tied in all four previous meetings this season. Former Barcelona forward David Villa hit the goal frame twice within the opening 20 minutes.
"We just have to keep working hard and stay calm because we still haven't won anything," Atletico coach Diego Simeone said.
AP Sports Writer Paul Logothetis in Madrid contributed to this report.