City took the lead after just three minutes, Kolarov smashing a left-foot free kick from the edge of the area into the top corner.
The home side pushed forward for further goals as they dominated possession and were denied a second when Simon Mignolet saved a point-blank shot from Pablo Zabaletta. Tevez, following up, fired across the face of goal.
Sunderland offered little going forward, their best chance in the first half coming when Stephane Sessegnon volleyed over when the ball fell to him from a free kick.
City continued to dominate in the second half as Yaya Toure saw a shot pushed over by Mignolet and Micah Richard's effort was cleared off the line by Danny Rose.
It was no surprise when City got a second, Sergio Aguero thumping the ball home on the hour mark from Kolarov's low driven cross.
The home side could have had more David Silva going close when his long-range chip came back off the crossbar.
James Milner put the icing on the cake late on when his free-kick took a slight deflection to beat Mignolet
Sunderland again found chances hard to come by, the best coming when James McClean's header from a corner was put over by Joe Hart.
The result represents City's best performance of the season, while Sunderland lose their unbeaten record.