Tevez, whose goals helped West Ham avoid relegation in 2007 before he moved to Manchester United, scored after five and 61 minutes as City completed a deserved win.
Monday's result rounded off an entertaining weekend of Premier League action with the 10 matches producing 37 goals.
Manchester United, 2-0 winners at Stoke City, top the table on 18 points, ahead on goal difference of Chelsea, who dropped points for the first time this season when they lost 3-1 at Wigan Athletic.
City's win took them to 15 points, alongside Tottenham Hotspur and Liverpool, who had thumping victories over Burnley and Hull City respectively. Arsenal and Aston Villa have 12.
West Ham remained third-last with four points from six games.
City, who won their first four league games of the season before their stoppage-time 4-3 defeat by Manchester United, were on top from the start at Eastlands.
They went ahead after five minutes when Martin Petrov squared for former Hammers hero Tevez to fire in from close range.
Tevez had two more good early chances before West Ham grabbed an unexpected equaliser after 24 minutes when a Radoslav Kovac shot was deflected in by striker Carlton Cole, only for Petrov to restore the lead eight minutes later with a well-struck free kick.
Man City took charge after the break and made it 3-1 on the hour when Tevez was left unmarked for the second time to head in a free kick from Craig Bellamy, another former Hammer.
Striker Roque Santa Cruz, bought for 17.5 million pounds from Blackburn Rovers, came on 10 minutes from the end for a belated debut but could not convert the once decent chance he got as City finished on top.
