Neymar’s first-half penalty helped ease the pressure on boss Thomas Tuchel as Paris-St Germain leapfrogged RB Leipzig in Group H of the Champions League.
The Brazilian scored his first goal in six matches in the competition after Angel di Maria had been fouled.
Julian Nagelsmann’s side rallied but some wasteful finishing prevented them from equalising.
Leipzig drop to third in the group and are three points behind leaders Manchester United with two games left.
The German club, who travel to Istanbul Basaksehir in their next fixture, were unfortunate losers to the side that knocked them out in last term’s semi-final.
Dayot Upamecano, Emil Forsberg and Marcel Sabitzer all went close to levelling the scores in an open contest that they grew into.
The only bright spot for the hosts, aside from Neymar’s goal, was the return of influential Italy midfielder Marco Verratti, who came on in the 83rd minute after a six-week injury lay-off.
Tuchel’s side face group leaders Manchester United at Old Trafford in their next group game.