Having been beaten by Liverpool before dropping points at home to Sunderland in a surprise 2-2 draw, City could ill-afford another slip-up at the Etihad Stadium.
While Manuel Pellegrini's men were not always at their fluent best, goals from the Argentinian trio of Pablo Zabaleta, Sergio Aguero and Martin Demichelis secured a welcome victory, leaving City a point adrift of second-placed Chelsea and six behind leaders Liverpool - with a game in hand on both.
David Silva's late withdrawal on a stretcher provided the only concern for City, who made a strong start and took the lead three minutes in when Zabaleta's acrobatic header evaded the attempted clearance of Craig Dawson.
Graham Dorrans produced a stunning half-volley to keep the visitors in the game during a frantic opening, but Demichelis restored his side's two-goal lead before the interval.
City, who brought Silva, Gael Clichy and Edin Dzeko into their starting XI, made an ideal start when Zabaleta followed up Aguero's saved effort to head home and settle any nerves at the Etihad.
West Brom then came close through Stephane Sessegnon's powerful drive before City went from the sublime to the ridiculous and gave their visitors the opportunity to pull a goal back.
In stark contrast to Wednesday's draw with Sunderland, there was little late drama for City, who appeared comfortable as the game moved towards a conclusion.
