Gabriel Jesus scored on his Premier League debut
Fonte was caught out of position and gave away a penalty on a nightmare debut for his new club.
City, who dropped Claudio Bravo and Sergio Aguero to the bench, took West Ham apart in the first half.
Kevin De Bruyne, David Silva and Gabriel Jesus on his first Premier League start scored before the break.
Yay Toure then slotted home a spot kick after 67 minutes to complete the scoring.
It was a miserable evening for Slaven Bilic as he watched on helplessly as Pep Guardiola’s men ran riot.
City moved level on points with Liverpool but stay fifth.