Michael Antonio and Pablo Fornals exploited slack defending to put the Hammers into a 2-0 half-time lead with Jarrod Bowen adding a third on the break in the second period.
City struggled to create chances throughout, only fashioning good openings in the final few minutes when the game was gone.
The win was West Ham’s second in a row, without conceding a goal as they now sit seventh in the Premier League table.
Leicester remain second on the league depending on the outcome of Liverpool match against Aston Villa later today.
Both Leicester and West Ham now head for the international break.
While Leicester have been brought back to earth after their strong start, West Ham can dream of a season that won’t end with them fighting relegation once again.
We’ll just have to wait and see.