An early finish from Sergio Aguero as well as a goal in either half from Yaya Toure - the second a penalty - put City three goals ahead and there was no way back for Albion despite a Costel Pantilimon own goal and a Victor Anichebe strike late on.
City had lost four of their six away games in the Premier League this season ahead of their trip to the Black Country, including their last two, but two early goals eased any nerves.
Aguero had already spurned one opportunity but made no mistake from a Pablo Zabaleta cross which he converted by firing high past Boaz Myhill inside 10 minutes.
Aguero was being partnered by Edin Dzeko in attack and the duo linked up well with plenty of support from midfield and - crucially - both full-backs too.
Midway through the first half it was the turn of Aleksandar Kolarov to advance down the flank and Toure let the ball come across his body before side-footing low into the far corner.
West Brom came into the game more in the latter stages of the first half with City restricted to counter-attacks but Morgan Amalfitano, Chris Brunt and Saido Berahino all fired wide from distance.
The pattern continued after the break with Shane Long seeing a penalty appeal turned down before the game seemed to turn decisively in City's favour when Chris Foy pointed to the spot at the other end.
Kolarov advanced into the box and went down under a challenge from Claudio Yacob on the corner of the area. Toure duly converted the resultant spot-kick by blasting the ball past Myhill for his second of the game.
Just as the home fans filed for the exit, substitute Matej Vydra saw his cross intercepted by Kolarov only to ricochet into the net off Pantilimon.
And Albion spirits were really raised when Anichebe held off a challenge from Martin Demichelis to reduce the deficit to just one goal in injury-time.
But there was no time for another attack with City getting the win to end West Brom's four-game unbeaten run at the Hawthorns - and their own away day blues.