Looking to overturn a one-goal deficit from the first leg, the Blues made a bright start at Old Trafford as Nicolas Anelka was just off target with two efforts from the edge of the area before Frank Lampard fired straight at Edwin van der Sar.
United thought they had snatched the lead when Javier Hernandez headed home, but the flag was up for offside and television replays showed the linesman had made an excellent close call.
However, the Mexican would not be denied a second time as United took a 2-0 aggregate lead just two minutes before half-time.
Anelka allowed Ryan Giggs to race onto the end of a smart pass from John O’Shea, and the evergreen Welshman produced a pinpoint pass for Hernandez to fire into the roof of the net from close range.
Chelsea boss Carlo Ancelotti responded by hauling off £50m signing Fernando Torres at half-time and replacing him with Didier Drogba, and the Ivorian looked to make an immediate impact as he forced Van der Sar into a decent save.
The veteran United goalkeeper, who will retire at the end of this season, was then called into action to deal with a Drogba free-kick, but the Blues’ task suddenly became more difficult when Ramires was sent off for a second bookable offence after a poor challenge on Nani.
Drogba gave them the perfect response 13 minutes from time when he chested down a Michael Essien pass and fired home, but less than 30 seconds later United wrapped up the tie when Giggs crossed for an unmarked Park Ji-Sung to score the winner on the night.