It was another impressive display from City, who maintained their challenge to break the monopoly of the big four.
But on the evidence of the spirited display from Gianfranco Zola's Hammers, it ought not to be long before they climb clear of the relegation places.
It was a match played at an electrifying pace with Martin Petrov, Craig Bellamy, Shaun Wright-Phillips and Tevez all blisteringly fast.
Tevez, whose only other City goal came in the Carling Cup, took little more than four minutes to make the breakthrough with a goal which owed much to the craft of Petrov, who provided the cross from the left for the Argentinian to slot home from inside the six-yard box.
It was very much a case of the Tevez show in the early stages as he could easily have scored a hat-trick in the opening quarter of an hour as he twice fired wide, the first one agonisingly so.
The Hammers, in danger of being completely overrun, stunned City with an equaliser out of nothing midway through the opening half when Carlton Cole diverted a shot from Radoslav Kovac wide of keeper Shay Given after Joleon Lescott failed to clear a free-kick.
City soon regained the lead when Petrov, replacing the injured Stephen Ireland, fired home a free-kick from 25 yards wide of the Hammers' defensive wall.
City could well have added to their goal tally before the break as Tevez, Bellamy and Petrov all had clear-cut chances as they regained control.
City sealed victory just after the hour-mark when Tevez scored his second goal of the game, a close-range header from Bellamy's free-kick.
The Hammers, to their credit, refused to concede defeat as Italian dangerman Alessandro Diamanti three times went close as did Mark Noble.
City handed a debut late on to Roque Santa Cruz, who had been plagued by injury since his summer transfer from Blackburn Rovers, and he almost marked his first appearance with a goal in the dying minutes when he fired narrowly wide from a Petrov cross.