James Collins looped an attempted clearance from a Jesus Navas cross into his own net to give City the lead.
Navas set up Sergio Aguero to slot in a second after a slick counter-attack.
With the game won, City playmaker David Silva was carried off on a stretcher after being caught in the face by Cheikhou Kouyate's right elbow.
Silva appeared to be given oxygen as he received eight minutes of treatment prior to his departure in the 75th minute.
Before the game, City boss Manuel Pellegrini conceded he could be sacked if his team do not finish in the top four to claim a Champions League place for next season.
But while speculation about his future continues given their tame title defence, the chances of missing out on a place in Europe's elite club competition receded with this victory.
With five matches remaining, Pellegrini's side are seven points clear of fifth-placed Liverpool, who have a game in hand, and a point behind derby rivals Manchester United.
City looked a vastly improved team to the one that had lost four of their past six league games, and more like the side that beat West Ham on the final day of last season to claim the Premier League title.
The Hammers, meanwhile, have won just once in their past 12 games, with their last away league win coming on 2 December.
From the outset, it seemed a question of how long West Ham could hold their dominant hosts at bay, and the answer was 18 minutes.
Navas swung in a low cross and, in attempting to clear the ball, West Ham centre-back Collins instead looped an effort over Adrian and into his own net.
The goal meant the Argentine was the first player to reach 20 Premier League goals this season.
Aguero had several chances to add to his tally, with one effort saved by the sprawling Adrian following an incisive move from Pellegrini's side.
West Ham had a late Kevin Nolan shot saved by Joe Hart, but they rarely threatened a comeback.
West Ham boss Sam Allardyce:
"The two goals we gifted them are pretty disappointing on the basis of how we conceded them.
"You can't make the mistakes we made and expect to get anything out of a game at Manchester City. We created our two best chances late on but can't seem to be as clinical as we used to be.
"The goal threat from us has not been as potent as we showed earlier on in the season."
It was 2-0 when Stewart Downing gave the ball away in the City half, the home side broke in lightning fashion and Aguero and Navas exchanged passes before the former slotted in.
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