The Citizens went down to two early goals from Thomas Mueller and Mario Goetze before David Silva pulled one back. In the second half, two goals in six minutes from the Manchester side by Aleksander Kolarov and James Milner secured the victory.
The win leaves Man City and Bayern level on points in Group D however Bayern's goal difference is higher meaning they will get the top spot. Elsewhere in Group D Viktoria Plzen beat CSKA Moscow 2-1.
Bayern Munich has been high flying in the league under new manager Pep Guardiola and is the favorite for many experts to win the Champions League for the second year in a row. Manchester City also has a new manager in Manuel Pellegrini who has led them to fantastic home form but the side has struggled on the road.