Manchester United's Champions League journey ended in Munich but David Moyes men can be proud of their efforts as they went down 3-1 (agg 4-2) to the reigning Champions at the Allianz Arena.
An uninspiring quarter-final, second leg burst into life when Evra met a bouncing ball with a rasping half-volley to put United ahead in the 57th minute and 2-1 in front on aggregate.
Mario Mandzukic equalised also immediately for Bayern with a header and Thomas Mueller turned in an Arjen Robben cross in the 68th minute before Dutchman Robben added the third himself.
Wayne Rooney had missed a chance to put United 2-1 ahead on the night when he scuffed a shot from in front of goal and Bayern went though 4-2 on aggregate to stay on course for a treble and continue United's miserable season.
As in the first leg that ended 1-1, Bayern totally dominated possession in the first half although they lacked fluency and struggled to create any real openings against a well-drilled United side who were always in the game.
Robben was Bayern's chief threat, getting into several promising positions after cutting inside on to his left foot in familiar fashion but his efforts were either blocked by defenders or flashed wide.
United had one opening when Rooney got clear of the Bayern defence but he dithered and failed to notice Shinja Kagawa in an unmarked position as the chance went begging.
The visitors went ahead in remarkable fashion when Antonio Valencia burst down the right and, although his cross went behind United's forwards, the lurking Evra lashed home a net-bursting effort from the edged of the area.
United's joy was shortlived though as Bayern replied immediately when Mandzukic got in front of Evra to score with a diving header after a Frank Ribery cross from the left.
That opened the game up completely and Rooney should have put United back in front but completely scuffed his shot with only Manuel Neuer to beat from 12 metres after Danny Wellbeck rolled the ball invitingly to him.
United were not given a second chance, as with 23 minutes left on the clock, Bayern struck the killer blow. Evra gave Robben the half-yard he needed to fire across the box and Muller swept the ball past De Gea after getting ahead of Vidic.
Moyes brought on Javier Hernandez, hoping the little Mexican could be his Ole Gunnar Solskjaer, but it was too late.
Robben's pace proved to be too much for Evra again. The Dutchman skipped past his marker and strode beyond Vidic before planting his finish into the corner, courtesy of a slight deflection off the Serbian, to signal the end of Moyes' hopes of silverware in his first season.
With the Bundesliga title already in the bag, Bayern can now look forward to challenging for more silverware in the coming weeks, but for United this defeat all but ended their season.
Seventh in the Premier League, David Moyes's side will almost certainly be missing from next season's Champions League.
Live coverage of the draw for the semi-finals of the UEFA Champions League from 10:55 on Friday 11 April on RTE.ie (RoI only).