The left back stunned the Allianz Arena with a fantastic effort to give David Moyes' side the lead, only for Mario Mandzukic, Thomas Muller and Arjen Robben to settle the tie
After a first half lacking in chances, Patrice Evra stunned the Allianz Arena with a wonderstrike from 25 yards to give the English side a shock lead, only for Mario Mandzukic to equalize just 73 seconds later.
The newly crowned Bundesliga champions then took control of the tie and were two goals to the good just 17 minutes later after Thomas Muller and Arjen Robben beat David de Gea from inside the area.
Bayern has now reached the semifinals of Europe's premier club competition for the third season in a row. The result signals an end to United's hopes of winning a trophy this season – something that has not happened since the 2004-05 campaign.
Mandzukic, Muller, Robben, Franck Ribery and Mario Gotze all started for Bayern in an aggressive lineup but it was the visitors who were able to create the first real chance.
United had the ball in the net in the 17th minute, but the goal did not stand with Antonio Valencia drifting into an offside position when converting a Rooney cross.
Bayern eventually recovered from its slow start and as expected, dominated possession, but it was frustrated by the Red Devils, who were happy to sit back and soak up pressure.
Clear-cut chances were few and far between, with Ribery and Toni Kroos both missing the target before the break, but the game burst into life after Evra's goal.
The left back ran onto a loose ball and hit a 20-yard left-foot rocket that flew into the top-right corner, an effort that gave Bayern goalkeeper Manuel Neuer no chance.
Bayern's reaction was outstanding, though, as it responded within 22 seconds from the restart through Mandzukic.
Ribery stood up a cross to the back post and the Croatia forward nipped in front of Evra to head past Manchester United goalkeeper David De Gea from six yards.
Bayern took the lead for the first time in the tie just nine minutes later, with Robben given too much time to cross on the right, and his low ball was swept home by Muller, who reacted quicker than Nemanja Vidic.
Robben then sealed the win with 14 minutes left, as he danced across the edge of the penalty area before shooting into the bottom-left corner, with the help of a Vidic deflection.
Substitute Claudio Pizarro had a late chance to extend Bayern's lead even further but his toe-poked effort was easily collected by De Gea.
It mattered little though, as Bayern's Champions League defense gathered more pace.