The host, which failed to get a single shot on target in the first half, fell behind to a Demy de Zeeuw strike in the 68th minute.
But Zlatan Ibrahimovic spared PSG's blushes from close range two minutes later with his seventh goal of the European campaign.
The result leaves the French side six points clear of third-placed Benfica, while Anderlecht, which had Sacha Kljestan sent off late on, can no longer qualify.
Laurent Blanc made five changes to the side that beat Lorient 4-0 in Ligue 1 last time out, the most notable of which was the return of Ibrahimovic in place of the injured Edinson Cavani (thigh).
Anderlecht, meanwhile, brought Dennis Praet into the starting line-up for Massimo Bruno after its 3-1 win against OH Leuven in the Belgian Pro League last weekend.
Ezequiel Lavezzi went close to breaking the deadlock for the host in the sixth minute, as he met a wonderful chipped ball into the area from Thiago Motta, only to nod narrowly over the crossbar.
As the half progressed, Group C's most potent attack struggled to find a way through its leakiest defence, and Anderlecht even managed to threaten at the other end - Aleksandar Mitrovic forcing Salvatore Sirigu into a diving save with a shot from the edge of the penalty area.
With the first period drawing to a close, Maxwell found himself in space on the left wing and tried to drill a low cross into the six-yard box, but Cheikhou Kouyate slid in superbly to put the ball behind and thwart the attack.
Ibrahimovic headed wide of Thomas Kaminski's right-hand post from a corner 10 minutes into the second half, which began in much the same vein as the first, with PSG dominating possession but failing to convert it into enough clear-cut chances.
Lavezzi tried to create an angle for himself in the penalty area nine minutes later, but Anthony Vanden Borre stuck a leg out to deflect the ball behind for a corner.
PSG was beginning to pile on the pressure, finding gaps in the thus-far resilient Belgian defence, and Lucas Moura was next to try his luck, blazing wide from a glorious chipped pass by Ibrahimovic.
But it was Anderlecht which broke the deadlock on 68 minutes with its first goal of the competition.
Kljestan found Demy de Zeeuw in space just inside the penalty area and he made no mistake in side-footing beyond Sirigu.
That lead did not last long, however, as Ibrahimovic found himself through on goal two minutes later and slid the ball under Kaminski and against the post, before pouncing to prod home from the rebound.
Kljestan was given his marching orders in the 82nd minute, picking up a second yellow card for a deliberate handball.