كتب : Sherif Tarek
Theo Walcott put the Gunners ahead on 18 minutes, before Florent Malouda scored the equalizer for the Blues 15 minutes later.
Ivory Coast skipper Drogba scored the winner six minutes from time.
Both sides were obviously exhausted following their UEFA Champions League triumphs.
Even though Arsenal got the upper hand in the second period, a deadly blunder by second-choice guardian Lukasz Fabianski enabled Drogba to net from a narrow angle.
Chelsea will face the winners of Sunday's semi-final between Manchester United and Everton.