City had to battle a dogged West Ham and blizzard conditions to edge a narrow 2-1 victory at the Etihad.
In freezing temperatures, Ilkay Gundogan gave City a first-half lead after good work by Riyad Mahrez.
And though chances came and went for the champions, sub Fernandinho's 90th-minute goal proved vital, with Manuel Lanzini pulling one back in added time.
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About the Official Man City YouTube Channel:
Here you will find all the latest videos from Manchester City, including, all Premier League goals, highlights, behind-the-scenes footage, training and much more.
Get closer to the likes of Jack Grealish, Kevin De Bruyne, Gabriel Jesus, Raheem Sterling, Riyad Mahrez, Phil Foden and the rest of Pep Guardiola's team.