Foden has 24 goals for City in all competitions this season and has often been utilised in more central roles by coach Pep Guardiola
Under fire from fans demanding new signings before the transfer window closes on Wednesday, Wenger was given some breathing space after Cazorla drilled in a ninth-minute penalty and Sanchez made it 2-0 in the 39th with a scrambled finish.
Halftime substitute Roberto Pereyra pulled one back for the home side on his Premier League debut when he curled in an unstoppable shot from 15 yards in the 57th minute after a pinball-style ricohet fell kindly for him.