A point in their final game at Watford on Sunday will now be enough to guarantee Pep Guardiola's side a place in the top four and Champions League football, while a win would see them finish third and go straight into the group stage.
This was as straightforward a victory as City could have anticipated at this stage of the season, as two goals in two first-half minutes put them in control against a Baggies side that lacked ambition and did not seriously threaten until the final stages.
First, Sergio Aguero's flick fed Kevin de Bruyne, who burst into the left-hand side of the area before squaring the ball to give Gabriel Jesus an easy tap-in.
One minute and 46 seconds later it was 2-0, thanks to a brilliant first-time finish from De Bruyne after Aguero's attempt to tee up Jesus was cleared into the Belgian's path on the edge of the area.
Yaya Toure made it 3-0 after the break, exchanging passes with Aguero as he marched into the area to slot past Ben Foster.
West Brom managed a late consolation when substitute Hal Robson-Kanu turned in Allan Nyom's low cross.