Sir Alex Ferguson fielded a second string side, but with the likes of Dimitar Berbatov, Antonio Valencia and Ji-Sung Park in the home side will have expected to progress.
Darren Ambrose gave the Championship side the lead in the second half, before Federico Macheda equalised for the hosts from the penalty spot and pushed the game into overtime.
Substitute Glenn Murray grabbed the all important winner after 98 minutes, and away manager Dougie Freedman was delighted with his team’s efforts.
“It is a wonderful night for the football club considering the position we have been in in recent years. We really enjoyed our night,” he told Sky Sports.
“We got the win, which I thought we deserved, we played some good football and showed desire to see out the game.
“When you come to Old Trafford you have to give everything you have got and the lads did that. We believe in each other and that takes you a long way at times,” he concluded.
Ferguson meanwhile apologised to the home supporters, and admitted his disappointment at being eliminated from the tournament.
“I’m so disappointed. I have to apologise to my fans and all the players who weren’t playing. We never expected that,” he said.
“Any time we go on the pitch it means a lot to Manchester United. We have our pride to protect and our history to protect. Every time we walk on the pitch it’s important. We didn’t see that tonight.
“Nine internationals out there. So that was a big disappointment.”
The draw for the next round has been completed also, and Crystal Palace will play against Cardiff for a place in the final, whilst Manchester City take on Liverpool.
By Gareth McKnight