|Robben pulled off a spectacular volley to put the German side into the last four [AFP]
A wonderstrike from Arjen Robben put Bayern Munich into the European Champions League quarter-finals as they dumped Manchester United out on away goals at Old Trafford.
Inspired by the almost miraculous early return of Wayne Rooney from the ankle injury he sustained in Munich last week, United rushed into a three-goal lead to put them on course for a last-four meeting with Lyon.
But Ivica Olic scored on the stroke of half-time in Wednesday's second leg and United were left hanging on when Rafael was sent off for a second yellow.
And when Franck Ribery swung over a corner, Robben was there on the edge of the box to execute a technically superb finish into the far corner to make it 3-2 to United, 4-4 on aggregate, with Bayern having scored two away goals to United's one.
Bordeaux beat Lyon 1-0 in the night's other match to give Lyon a 3-2 aggregate win.
At Old Trafford the night started perfectly for United, who had conceded a late goal to start 2-1 down from the first leg.
In the fourth minute Brazilian right back Rafael found Rooney with an inventive infield pass.
The England striker touched the ball on to youngster Darron Gibson, who hammered past an astonished Jorg Butt.
Just four minutes later United were two up when Antonio Valencia toyed with the defence before crossing for Nani to touch the ball into the corner with his trailing leg as the centre backs gaped.
And Nani was on hand again on 41 minutes to put United three up and seemingly cruising, side footing a Valencia cross into the roof of the net.
But two minutes later Olic beat Michael Carrick to a header in the box and drilled past Edwin van der Sar to give the visitors a crucial away goal.
And when Rafael was sent off after the second of two needless yellow cards, United were fighting not to concede until Robben intervened with just over 15 minutes to go.
"When we were behind 3-0 I thought it was going to be a very difficult evening. But 3-0 was the same as 2-0. We had to score a goal," Robben told German TV.
"The goal from Olic gave us faith that we could still advance. We have to be honest. They were the better team at the start, with the atmosphere.
"I saw that Franck saw me at the corner. I knew the ball would come across to me. I tried to stay calm. You can use force or technique. I tried to use technique. It worked out."
First for Lyon
Lyon reached the Champions League semi-finals for the first time despite losing 1-0 at French rivals Bordeaux.
Ligue 1 champions Bordeaux had only an outside chance of qualifying after going down 3-1 in Lyon last week but Morocco striker Marouane Chamakh kept their hopes alive by scoring from close range just before the break.
Lyon, though, controlled much of a highly-tactical affair that was not as exciting as the first leg to triumph 3-2 on aggregate and set up a meeting with Bayern.
Chamakh volleyed wide from a Benoit Tremoulinas cross before Bordeaux rattled the bar with a powerful 30-metre shot from Alou Diarra.
Seconds later a low cross by Tremoulinas took a deflection and Chamakh pounced to score from close range.
Bordeaux had most of the possession in the second half but rarely looked like grabbing a second goal.
The home fans shouted for a penalty after a challenge on Chamakh from Brazilian defender Cris but the referee waved play on.
Bordeaux then gave the visitors a scare in the dying moments when a header by Brazilian midfielder Wendel forced a brilliant save from France keeper Hugo Lloris.