Laurent Blanc's men twice took the lead in the first half, through Hervin Ongenda and Jean-Christophe Bahebeck, but were ultimately punished for some sloppy defending.
Terrence Boyd and Yussuf Poulsen each found equalisers for the hosts, who duly prevailed courtesy of a 65th-minute volley from Denis Thomalla and Marquinhos' subsequent own goal.
In front of a healthy crowd in Leipzig, the hosts - who are preparing to play in Germany's second tier for the first time this season - more than played their part in an open first period.
An unmarked Ongenda was left with a simple finish to open the scoring after 10 minutes, having been picked out by Clement Chantome's square ball.
Boyd replied from close range after Nicolas Douchez had made a fine save to keep out Joshua Kimmich's initial header, but PSG - with Zlatan Ibrahimovic featuring from the start - re-took the lead almost immediately as Bahebeck beat goalkeeper Fabio Coltorti to head home a cross from Ongenda.
Ibrahimovic was guilty of a poor miss before Poulsen converted a right-wing corner six minutes after the interval to make it 2-2.
Leipzig then moved in front, Thomalla capitalising on more generosity from PSG's back-line, and Marquinhos deflected substitute Stefan Hierlander's effort past his own goalkeeper as Leipzig claimed a notable scalp.
'I’m not a start-stop player – it is so hard for me to influence a match from the bench and then be on the bench again, and then two weeks later I start again': Thomas Tuchel reveals what England star told him following squad announcement
'I almost feel a little bit sorry for Mohamed Salah': Jamie Carragher sounds Liverpool alarm bell following Carabao Cup final defeat
