James Collins gifted the home side the opener with an own-goal after 18 minutes and Sergio Aguero added a second before half-time.
The result sees City reduce United’s lead over them to just a single point, after the third-placed side lost 1-0 at Chelsea on Saturday evening.
A real concern for City, however, will be the injury suffered by David Silva, who was forced off on a stretcher after taking an elbow to the face from Cheikhou Kouyate midway through the second half.
After the 4-2 dismantling at Old Trafford last weekend, Manchester City could not have wished for a better game in which to bounce back than at home to West Ham – who from the first whistle had the look of a team who knew their season was already over.
The first sign of danger for the Hammers came within five minutes when Silva got in behind their defence and managed to bring a pass down from Martin Demichelis, but the Spaniard couldn’t quite get his shot away before he was blocked off.
Sam Allardyce’s side looked well off the pace and their sloppy play at the back saw them give the ball away on more than one occasion in the early stages, a trait that led to both goals they conceded in the opening half.
First, Adrian’s goal kick that barely reached the halfway line was picked up by Navas, who charged forward menacingly. His cross from the right was poor and only reached defender Collins, but the Welsh international got his feet into a major muddle and somehow managed to slice the ball over his own keeper under no real pressure.
Then, with less than 10 minutes until half time, Stewart Downing relinquished possession on halfway, only for Aguero to pick it up and skip past Collins before driving at the heart of West Ham’s defence.
The Argentine then played a little one-two with the lively Navas before finishing calmly from close range. City were two up and cruising.
And they continued to dominate after the break, with Aguero and Silva both having chances that they couldn’t quite convert for a City third.
On the whole it was a satisfying afternoon for Manuel Pellegrini, with the only real negative from the game being the injury to Silva after his collision with Kouyate.
The West Ham midfielder was booked for his troubles but he could easily have seen red for a challenge that saw the City midfielder taken off on a stretcher to a warm ovation from all corners of the Etihad after seven minutes of treatment.
Understandably, the game lost a little momentum after the injury to Silva and other than a decent chance for Enner Valencia the home side never looked in any real danger, cruising to a victory that also sees them extend their gap over fifth-place Liverpool to seven points.
Man City: Hart (6), Zabaleta (7), Mangala (6), Demichelis (6), Kolarov (6), Fernando (7), Lampard (6), Toure (7), Navas (8), Silva (7), Aguero (8)
Subs: Fernandinho (5), Nasri (5), Dzeko (5)
West Ham: Adrian (5), Jenkinson (5), Reid (5), Collins (4), Kouyate (4), Song (4), Noble (5) Downing (4), Valencia (6), Cole (3)
Subs: Jarvis (5), Nolan (5)
Man of the match: Sergio Aguero