The Sky Blues scored their first thanks to a precise through ball from Kevin De Bruyne that was latched onto by Fernandinho.
De Bruyne then got in on the act in the second-half, finishing off a sumptuous counter-attack with a tap-in.
Raheem Sterling set-up Sergio Aguero for the killer blow with a delightful reverse pass with one minute remaining in normal time.
West Brom loan signing Daniel Sturridge made an appearance late on.
The win solidifies City's standing at the top of the Premier League table as their rivals continue to drop points.