Unlike Tottenham Hotspur vs. Burnley which was postponed earlier in the day, the match in Manchester went ahead but it was difficult at times to see the pitch through the flurries of snow. The start of the second half was delayed by five minutes as groundstaff sought to clear the pitch.
City took a short corner which West Ham defended but only momentarily, allowing Fernandinho to get a low shot off on goal.
West Ham did have a few promising attacks with one of the most frustrating chances coming in the second half seeing Vladimir Coufal and Michail Antonio both going for the same ball allowing City the chance to clear and avert danger.
They finally scored deep into added time when Manuel Lanzini dispossessed Fernandinho and volleyed the ball off the post and into the net.
The win sees City overtake Liverpool into second place in the Premier League table while West Ham lose further ground on the top three, now five points off the Merseyside club.