The visitors took the lead through Demy De Zeeuw with a little over 20 minutes remaining before Ibrahimovic scored the equaliser two minutes later.
Things got harder for the visitors when Sacha Kljestan was dismissed with eight minutes remaining but they held out for a draw.
Ezequiel Lavezzi had the first chance of the game but with Thomas Kaminski rushing out of his goal the Argentina international missed the target.
With 11 minutes gone Lavezzi had another chance but after taking a fine first touch he was crowded out by two defenders.
Ibrahimovic could also have given the home side the lead but fired over the bar from 15 yards.
Anderlecht's first real chance fell to Aleksandar Mitrovic but after doing well to control the ball on the edge of the area his well-struck shot went over.
The same player worked space in the area shortly afterwards but shot straight at Salvatore Sirigu in the PSG goal.
Then Anderlecht's Dennis Praet found space at the back post but fired his volley wide from a cross by Chancel Mbemba.
Anderlecht continued to exert pressure up to half-time but Mitrovic fired over the bar in added time as the first half drew to a close.
Ibrahimovic fired in a free-kick from long range early in the second half but the danger was cleared.
Lavezzi saw his shot blocked by Anthony Vanden Borre following a counter-attack and Ibrahimovic shot just wide and then set up Lucas but he was also off target.
With 68 minutes gone the away side took the lead through De Zeeuw to give the Belgian club their first goal in the group stages.
A fine move saw Kljestan pass to De Zeeuw and he found the net with a low shot.
But PSG were level two minutes later as Ibrahimovic netted despite the best efforts of Kaminski. The keeper did well to deny the striker from close range but the ball hit the post and fell to the Swede, who made no mistake.
Things got worse for Anderlecht with eight minutes remaining as Kljestan was dismissed after being booked for handball. The United States international had also been cautioned in the first half for a foul on Lucas.
Lucas tried to make the most of the one-man advantage but shot wide before substitute Javier Pastore saw his effort saved by Kaminski as the visitors held on.