The results saw Manchester seize the top of the league. United maintained first place with a 2-0 victory over Sunderland and City leapt into second with their 3-1 win at Newcastle.
Manchester United 2 Sunderland 0: Dimitar Berbatov two good but Red Devils stuck in cruise control Head boy: Berbatov nods United ahead
Tevez produced a child's dummy as a goal celebration - a tribute to his two daughters in South America. He now has 12 goals this season and these were his first since an aborted attempt to leave the club. They came against Newcastle's Alan Pardew, with whom he had a fractured relationship during their days at West Ham.
At least Roberto Mancini's rapport with Tevez appears mended.
The two shook hands when the smiling striker was substituted and Mancini said: 'Everything is finished with Carlos. We are all just focusing on the season and he is as focused as all of us. I was impressed with his performance today, but I like the way all the team played. It was very important after the Everton defeat.'
Enlarge Reach out: Captain Tevez stretches to double Manchester City's lead and give Newcastle a mountain to climb
Cole's goals saw West Ham replaced by Wolves at the bottom of the table and Van der Vaart helped Tottenham stay fifth, ahead of Bolton.
Newcastle 1 Manchester City 3: Carlos Tevez keeps City in the hunt with double to down Magpies Bolton 2 West Bromwich 0: Taylor and Elmander punish wasteful BaggiesManchester United 2 Sunderland 0: Dimitar Berbatov two good but Red Devils stuck in cruise controlFulham 1 West Ham 3: Cole at the double to help Hammers move on upVilla 1 Tottenham 2: Brilliant Van der Vaart at the double for ten-man SpursWolves 1 Wigan 2: Rodallega and Cleverley condemn McCarthy's menBlackburn 0 Stoke 2: Huth and Wilson hand Kean a baptism of fire
Explore more:People: Carlos Tevez, Carlton Cole, Dimitar Berbatov, Roberto Mancini Places: Newcastle, Manchester