An early strike from Sergio Aguero and two goals for Yaya Toure, including a second-half penalty saw City to a victory at The Hawthorns which kept them six points adrift of leaders Arsenal.
However the night, ended on a disappointing note for the visitors as goalkeeper Costel Pantilimon scored an own-goal and Victor Anichebe reduced the arrears in the last five minutes.
The match in the West Midlands was delayed by 15 minutes due to an accident on the M6 motorway which held up a large number of supporters.
But City made light of the late start and began the game at speed with Samir Nasri shooting just wide within seconds. A second warning shot from Manuel Pellegrini's side was not heeded shortly afterwards as Aguero fired just wide after Edin Dzeko had linked up well knocking the ball down into his path.
The Argentine was to open the scoring in the ninth minute. Dzeko's through ball found Pablo Zabaleta who crossed for Aguero and he coolly converted for his 17th goal of the campaign.
Saido Berahino was handed a surprise start, just two days after signing a new three-and-half year contract, and he came closest to getting the hosts back in it when he fired fractionally wide from outside the area.
But it was City who provided most of the clinical attacking threat with Aguero missing the target again from another knockdown from Dzeko.
A second goal for the visitors duly arrived in the 24th minute and it was a well-worked team move, Aguero finding Nasri who in turn fed Aleksandar Kolarov who crossed for Toure to skilfully beat Boaz Myhill for his eighth goal of the season.
It could have got even worse for West Brom soon afterwards with Myhill making a brilliant stop to push Aguero's effort around the post after the Argentine had found himself in plenty of space down the right.
West Brom looked for a way back into the game but when they did attack, City captain Vincent Kompany, making his first appearance since October 5, and Martin Demichelis were not afraid to put in the tackles.
But West Brom showed they could be a threat of their own when Kompany tangled with Shane Long, but referee Chris Foy waved away convincing penalty appeals from home players and fans alike.
However, Kompany generally marshalled his defence well on his return from injury. Baggies boss Steve Clarke sent on Anichebe for Long and handed a welcome return to midfielder Zoltan Gera for James Morrison in a bid to find new ideas and varied attacking threat.
It was the Hungarian's first appearance at The Hawthorns since he sustained a serious knee ligament injury in a FA Cup match with Queens Park Rangers in January.
West Brom did not appear likely to get back into the contest but it was Toure who sealed victory with a controversial penalty. Claudio Yacob appeared to win the ball in a tackle with Kolarov but Foy pointed to the spot.
Ivory Coast star Toure emphatically converted the spot-kick, sending Myhill the wrong way in front of the City fans behind the goal. But West Brom scored five minutes from time as Pantilimon got the final touch after Kolarov had not cleared from substitute Matej Vydra's cross.
Pantilimon's error fuelled the debate over the club's goalkeeping situation at City after England international Joe Hart was dropped recently by Pellegrini.
Deep into stoppage time, the hosts reduced City's lead to 3-2 when, with Vydra again the creator, former Everton striker Anichebe slotted home his first West Brom goal.