كتب : Omar AbdelAziz
The Premiership top scorer fired home in the second period of extra time to give his side their vengeance from the newly-crowned Premiership champions who dethroned the Blues following their two-year triumph under Jose Mourinho.
Chelsea's victory reaffirms their domination over English cups this season after they clinched the Carling Cup, beating Arsenal 2-1 in February with the extraordinary Drogba netting the winner as well.
A dull 90-minute stalemate was forced into extra-time, after both sides failed to create much danger on both goalkeepers, with the long season showing its effect on some tired legs at both ends.
Ryan Giggs came close to snatching an extra-time winner, but his close range effort was blocked bravely by Petr Cech as the ball looked to have crossed the line but it was a result of Giggs' clear foul on the Czech guardian.
The Blues responded later with a shot from Ivorian forward Salomon Kalou, that went inches wide of Edwin Van der Sar's goal.
Both sides looked set for a penalty shootout finale to their intense season, but Drogba had the final word four minutes before the end to maintain his remarkable form with Chelsea this term.
John Obi Mikel found Drogba at the edge of United's area, and the former Marseille man exchanged a brilliant pass with Frank Lampard, before slotting home with a trademark finish from 10 yards out.