Drogba completed the rout with a second goal of his own on a free kick late in the second half.
Arsenal manager Arsene Wenger was aggrieved that a goal by Andrei Arshavin early in the second half was disallowed for a foul by Eduardo on Petr Cech.
"It was a Chelsea player stopping the ball," Wenger said. "The referee made a massive mistake when you start the second half at 2-1 instead of 2-0 it's psychologically important."
Chelsea manager Carlo Ancelotti rejected suggestions that his team's muscle won the game.
"We have a physical quality," the Italian said, "but we have other qualities too. Our midfield won the game and we defended with intelligence. It's true that Arsenal kept the ball for the first half but when we got possession we were very good on the counterattack."