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.
The right-back was quick to react after Ben Foster had parried a shot from Aguero and the striker added a second goal seven minutes later.
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.
The win keeps City in with a fighting chance of claiming the title, while West Brom remain two places and three points above the relegation zone having played one game fewer than the three sides immediately beneath them.
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.
Aguero spooned another effort over the bar on only his second start after returning from injury, but soon shook off any rustiness to score his first goal since January, a low shot from outside the area beating Foster as the goalkeeper dived to his left.
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.
A shambolic free-kick routine saw City concede possession and, when West Brom broke, Matej Vydra slipped in Dorrans, who juggled the ball superbly past Clichy and fired home.
Despite struggling to find the fluency they had demonstrated early on, City scored again nine minutes before the break.
Demichelis joined countrymen Zabaleta and Aguero in getting on the scoresheet, finding the net from close range after Vincent Kompany had flicked a corner into his path.
Kompany made a fine block to deny Sessegnon before half-time, but the second period provided much less in the way of excitement.
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.
However, their evening was soured when Silva was taken off injured with his right leg in a brace following an innocuous challenge with Billy Jones.
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