City need a point from their final match to be absolutely sure of Champions League football after they beat West Bromwich Albion 3-1 while fifth-placed Arsenal stayed in the hunt by beating relegated Sunderland 2-0.
Gabriel de Jesus, Kevin de Bruyne and Yaya Toure scored City's goals as they moved two points above Liverpool in third.
With a superior goal difference of five to that of Arsenal, who are three points behind, it would take a big turnaround to deny City.