Although Dzeko's penalty following Koscielny's red card was turned onto the post by Wojciech Szczesny, with the Arsenal goalkeeper gathering the rebound, it was not long before Milner and Dzeko himself made the man advantage count.
The visitors too were a man down at the Emirates Stadium when, 15 minutes from time, City captain Vincent Kompany was dismissed by referee Mike Dean for a challenge on Jack Wilshere despite appearing to win the ball first.
Second-placed City were briefly 10 points adrift of United after their cross-town rivals beat Liverpool 2-1 at Old Trafford earlier on Sunday.