Rooney, returning to the heat of battle just eight days after damaging ankle ligaments in his side's 2-1 defeat in the first leg of their quarterfinal, flummoxed Bayern by his mere presence as United romped to a 3-0 lead but ultimately his amazing powers of recovery counted for nothing.
The England striker, who has scored 34 goals to underpin United's season, was largely a peripheral figure as United scored three goals in the opening 41 minutes against a Bayern side that had completely fluffed their lines amid the tumultuous din of a heaving Old Trafford.
He had a hand in Darron Gibson's opener after three minutes but after that it was Antonio Valencia and Nani who tore Bayern to shreds, the latter scoring twice to send United seemingly toward a fourth consecutive semifinal in the competition.
That was as good as it got, however, for United, who conceded twice to crash out on the away goals rule - the second, former Chelsea winger Robben's killer blow, coming after Rooney had trudged off after 55 minutes with more damage to his ankle and Brazilian fullback Rafael had been sent off.
As the Old Trafford crowd disappeared into the night, the realization that their team relies too heavily on Rooney was nagging away again.
Despite the striker not firing on all cylinders, United were full of pace, passion and purpose for most of his 55 minutes.
After that, although hampered by going down to 10 men, they retreated into their shells and to such an extent that Robben's knockout blow was hardly a surprise.
"I was confident we could score the goal in the second half," Bayern's Dutch coach Louis van Gaal told reporters. "It was incredible to come back from three goals down.
"The goal from Robben was unbelievable." Van Gaal refused to enter a slanging match with United boss Alex Ferguson who accused Bayern of getting Rafael sent off after 50 minutes when he tugged the shirt of Franck Ribery and also dismissed Ferguson's gripe that Rooney had been roughed up.
"I don't share his opinion," Van Gaal said of Ferguson's rant at Rafael's red card. "Part of the professional game is control and every player must know that if you pick up one yellow card a second one means a sending off." He preferred to savour an aggregate victory that ended a run of four quarterfinal defeats for Bayern, who last won the competition in 2001, and the prospect of a semi-final with Lyon.
Ferguson was left to ponder an evening that started full of hope but ended with the worrying prospect of the League Cup, England's least important trophy, being United's only silverware in a season that until last week promised a treble.
"In one way I could say we threw it away in another I could say we were very unlucky," Ferguson told reporters. "We could have been four or five up at halftime but they scored before the break and it was a crucial blow for them." Seven turbulent minutes was all it took for a rampant United to turn a 2-1 first leg deficit into a 3-2 aggregate advantage at the Theatre of Dreams - reviving memories of the 7-1 rout of Roma at the same stage three years ago after they had also lost the first leg 2-1.
Rooney's most telling touch of the night sent Darron Gibson through to strike United in front after three minutes and Nani's deft back heel from Valencia's cross made it 2-0 as Bayern buckled in an electrifying atmosphere.
The visitors looked dead and buried when Nani struck again after 41 minutes with a magnificent shot into the top corner but Croatian Ivica Olic, scorer of the late winner in Munich, grabbed one back two minutes later from a narrow angle to give his side hope at the interval.
Five minutes into the second half, Rafael's inexperience resulted in a second yellow card - the turning point, rather than Rooney's withdrawal soon afterwards, according to an angry Ferguson who pointed the finger at Bayern's players.
"They got him sent off, there's no doubt about that," he said. "After that they had control of the ball that they never had all night." Robben, who used to terrorize defenses in the Premier League in Chelsea colours, was unshackled in the second half, wreaking havoc down the right as United went slowly backwards.
When a corner from Ribery was lofted toward him after 74 minutes, time seemed to stand still before one swing of his left boot sent the ball hurtling past Edwin van der Sar.
