The Bundesliga giants, hoping to win by four goals to claim top spot in the group, got off to a perfect start by breaking the deadlock on eight minutes.
Kingsley Coman flicked the ball over the PSG defence to Robert Lewandowski just inside the six-yard box and the Polish striker made no mistake from close range.
Bayern then doubled their lead in the 37th minute through Corentin Tolisso, who rose highest in the area to connect with a James Rodriguez cross, heading beyond Alphonse Areola low into the visitors’ net.
The Ligue 1 side managed to halve the deficit shortly after the restart, however, as Kylian Mbappe was given time and space on the edge of the six-yard box to head home Edinson Cavani’s delivery.
Nevertheless Tolisso restored Bayern’s two-goal lead on 69 minutes, latching on to Coman’s cutback before coolly slotting past Areola.
Despite losing the match, PSG were able to stop Bayern from winning by four goals, ensuring that Unai Emery’s side would finish top of the group.
Paris Saint-Germain have finished top of Champions League Group B despite succumbing to a 3-1 defeat to Bayern Munich in Tuesday night’s encounter at the Allianz Arena.