Both sides saw key players ruled out through injury ahead of the game, with City captain Vincent Kompany still injured from the midweek Champions League game against Juventus.
David Silva was injured in the warm-up and was replaced by Jesus Navas, while the Hammers were without key defender Angelo Ogbonna and crucial midfield star Cheikou Kouyate.
Home crowd stunned
Moses stunned the home crowd by scoring the first goal against the Blues in the Premier League this season, collecting the ball from Dimitri Payet 30 yards out, advancing and unleashing a wicked low shot into Joe Hart's bottom corner on five minutes.
It was soon 2-0 when City failed to clear a corner and it fell to Sakho who slotted home a neat finish under pressure inside the six-yard box.
Mangala tackle could prove pivotal
The Hammers, who have beaten Arsenal 2-0 and Liverpool 3-0 in their previous away games so far this season, could have made it 3-0 when Sakho got through but Mangala made a brilliant last-ditch tackle.
West Ham tired as the half wore on, though, and City upped the ante in a desperate attempt to get back into the game.
And they did just that in first half stoppage time, new big-money midfielder Kevin De Bryne finding himself unmarked on the edge of the box and drilling low past Adrian.
West Ham will have to put in a real shift to withstand the expected Blue wave of attacks in the second half but will pose a major threat on the counter attack.