Kylian Mbappe and Marquinhos were on target for the Parisiens, leaving the reigning European champions with an uphill battle in the second leg next week.
Mbappe and Marquinhos each scored a goal in the first half to give the visitors an emphatic 2-0 lead. However, former PSG striker Eric Maxim Choupo-Moting reduced the deficit just before the break.
Thomas Muller then scored with a smooth header at the hour mark to pull the holders level. However, Mbappe rounded off a stunning counter just minutes later to hand his side another vital away win.
PSG take a commanding lead into next week's home leg. However, given the nature of this tie so far, we can certainly say that it is far from over.
Here are the hits and flops from the match:
Hit: Kylian Mbappe (PSG)
Kylian Mbappe was on fire once again as he lit up the snowy Allianz Arena with his scorching display.
With two more goals on the road, the young Frenchman proved that no defense is mean enough to stop him, not even that of the reigning treble winners.
Both of his strikes on Wednesday came on the counter. However, the second goal was truly remarkable as the forward slalomed past a stream of red shirts before firing a shot into the back of the net.
Flop: Leroy Sane (Bayern Munich)
Leroy Sane is having a somewhat decent debut campaign with Bayern Munich, though his record in the big games leaves a lot to be desired.
Once again, in a top-billing Champions League encounter, the former Manchester City star dropped a stinker and was unable to affect the proceedings in any way.
The 25-year-old misplaced plenty of passes. Of the meager two shots he mustered at goal, one was off target, and the other was blocked.
From a creative perspective, Sane lacked any sort of imagination while trying to take up positions in PSG's defense and mostly played his passes sideways.