Demy De Zeeuw opened the scoring for the Belgians in the 68th minute, only for Ibrahimovic to equalise two minutes later from inside the area.
Anderlecht were reduced to 10 men in the 82nd minute when Sacha Kljestan was shown a second yellow card, but the visitors, who lost 5-0 at home to PSG two weeks ago, held firm.
The French side lead Group C with 10 points from four games, three ahead of Olympiakos who beat Benfica 1-0. Benfica have four points and Anderlecht are bottom with one point.
"I would not say we lacked the desire to play," PSG coach Laurent Blanc told a news conference.
"We were too average in all departments, we were not good technically, which had not happened to us in a along time.
"Anderlecht were rewarded for their efforts. They are good, well-organised team."
"We faced a team looking to avoid defeat and we did not do what we had to do," said PSG midfielder Blaise Matuidi.
"We would have liked to qualify tonight but I think we will do it next time."
PSG next face Olympiakos at home in three weeks and Anderlecht host Benfica.
"The first leg helped us grow and tonight we can be disappointed that we did not take all three points," said Anderlecht defender Fabrice N'Sakala.
"It is not PSG who were different, it is us who defended better," said coach John van den Brom.
Two weeks after their Brussels stroll, PSG did not have it all their way at the Parc des Princes.
Despite their early domination, PSG failed to break the deadlock in the first half as Lucas, who was in the starting line-up after Edinson Cavani was ruled out injured, lacked accuracy.
Ibrahimovic came close 10 minutes into the second half with a downward header shortly before Lucas volleyed just wide from the Swede's cross.
Anderlecht went ahead against the run of play when De Zeeuw slotted the ball past Salvatore Sirigu after connecting with Kljestan's back pass.
The visitors barely had time to celebrate as Ibrahimovic cut through the defence and his shot was deflected on to his right post by Thomas Kaminski, but the former AC Milan and Barcelona forward had followed and poked in the rebound.
It was Ibrahimovic's seventh goal in this season's Group stage.
Kljestan picked up a second yellow card for handling the ball in the 82nd minute.
Centre back Thiago Silva came on in the 62nd minute for Marquinhos, making his return from a six-week injury layoff. The Brazil international had a great chance in stoppage time but his header was blocked by Kaminski.
- Sports & Recreation
- Sacha Kljestan
- Demy De Zeeuw