After being undefeated in ten previous semi-finals, the Red Devils were finally undone as Chelsea remain on course for an unprecedented quadruple.
Having been held to a goalless draw at home in the first leg, Chelsea produced a professional display at Old Trafford where they gave manager Jose Mourinho a perfect 42nd birthday present.
With a place in the final at Cardiff's Millennium stadium at stake for the winners, both teams fielded their big guns, though United left Wayne Rooney on the bench as they opted for a 4-5-1 formation.
Chelsea took the lead in the 29th minute after a clinical move involving Arjen Robben and Didier Drogba, with Frank Lampard ghosting into the penalty area to fire low past keeper Tim Howard.
The home side failed to trouble Chelsea keeper Petr Cech in the opening 45 minutes, though they had a strong shout for a penalty turned down following a challenge by Wayne Bridge on Quinton Fortune.
United's exit would have been sealed midway through the second period but for two great saves from Howard.
The American denied Lampard and Robben and the importance of those saves were shown moments later when Ryan Giggs equalised with a delightful chip over Cech from Gary Neville's cross.
Damien Duff sealed victory in the 85th minute scoring directly from a free-kick from 40 yards out on the right wing. He floated in a cross which eluded everybody and bounced pass Howard into the roof of the net.
United staged a storming finish and were desperately unlucky not to equalise.
Mikael Silvestre stole in to meet Giggs' corner and his header beat Cech only for Bridge to clear off the goal-line.
And right at the death Cristiano Ronaldo fired in an angled shot from the right, which Cech kept out with a brilliant diving save.