Chelsea dominated the game and Drogba scored after 30 and 33 minutes but City were fuming about the second goal, which was scored with the aid of a handball.
City defender Sylvain Distin was sent off as the teams walked off at halftime for complaining about it, having been booked for doing the same when the goal was scored.
Chelsea, beaten by Fulham last week, move to 78 points, 14 ahead of Liverpool, who overcame an 18th-minute red card for captain Steven Gerrard to beat Everton 3-1 at Anfield.
Results:
Aston Villa 0 Fulham 0
Chelsea 2 Manchester City 0
Liverpool 3 Everton 1
Sunderland 0 Blackburn Rovers 1
Wigan Athletic 1 West Ham United 2
—Agencies