Goals from Gabriel Jesus, Kevin De Bruyne and Yaya Toure did the damage and although Hal Robson-Kanu netted a late consolation, the game was effectively already over as Pep Guardiola's side got to within a point of sealing a spot in next season's Champions League.
It took City some time to get going in front of a less-than-capacity crowd in the North-West, but after Aleksandar Kolarov's free kick was saved in the 14th minute, it was one-way traffic.
After De Bruyne reached the byline, his deflected cross found Jesus all on his own at the back post and he could not miss from just two yards out.
Two minutes later, City effectively ended the match as a contest - even with 29 minutes left - when De Bruyne lashed the ball into the bottom corner from 20 yards after the ball had deflected into his path.
The home side should have been at least three goals to the good before the break but after De Bruyne and Aguero both saw long-range strikes comfortably saved by Ben Foster, Sane drilled a half-volley over the bar.
Like in the first half, City did not immediately set about pushing for goals but within 12 minutes of the restart, they found a third through Toure who confidently placed the ball past Foster after playing a one-two with Aguero.
A number of substitutions disrupted the flow of the match - with Pablo Zabaleta introduced for his farewell appearance at the Etihad - but it was then when West Brom looked most dangerous with Rondon heading just wide of the post from 12 yards.
Apart from his goal, Jesus had been quiet but he almost scored a stunner after deceiving three West Brom defenders before seeing his well-struck strike tipped over by Foster.
City took their foot off the gas with the match seemingly over as a contest, with only Jesus forcing two excellent saves out of Foster after he had been found on the right.
However, with three minutes left, West Brom surprised their hosts with a goal as Allan Nyom found Robson-Kanu in the middle and he did the rest from six yards out.
It mattered little as City were able to see out the remaining minutes to move to the brink of guaranteeing their position at European football's top table for the next campaign.