City found themselves a goal down after 10 minutes when Dani Olmo found the net with a sumptuous volley, before Gabriel Jesus took centre stage.
The Brazilian headed an equaliser just after the half-hour mark and doubled his account with a sublime individual effort early in the second period.
With Phil Foden rounding off the scoring for City late on after being handed a rare start.
Sterling failed to add to his five European goals this season, despite getting himself into a goalscoring position on several occasions.
The 25-year-old referenced once such occasion in a Tweet after the match, highlighting the bizarre look on his face as he bore down on the Zagreb goal.
Sterling posted three images of himself with the caption ‘Phil Jones would be proud’, in reference to the United defender’s well-documented history of unfortunate facial expressions.
Earlier this year Jones revealed that he has often been the butt of jokes among his team-mates at Old Trafford and on the international stage with England.