Sweden striker Ibrahimovic was shown a straight red card 21 minutes from time after a high kick on keeper Stephane Ruffier's chest as he was chasing the ball.
PSG, who have 22 points from 11 games, were already 1-0 down after Mamadou Sakho had deflected a Pierre-Emerick Aubameyang cross into his own goal 10 minutes into the second half.
Aubameyang put the result beyond doubt in the 73rd, beating Salvatore Sirigu from close range after being set up by Alejandro Alonso.
Striker Guillaume Hoarau pulled one back with two minutes left when he controlled the ball from a Javier Pastore free-kick before firing past Ruffier.
"The red card is not deserved because he was not looking at the keeper, but at the ball," coach Carlo Ancelotti was quoted as saying by French media.
"In the dressing room, he did not say anything, he was disappointed. But the problem was before [the red card]. We had no pace. Saint-Etienne played better than us and they deserved to win."
PSG suffered a double injury blow in midfield as Blaise Matuidi was replaced by Bodmer shortly before half-time and Clement Chantome suffered a possible ankle injury and was substituted by Mohamed Sissoko after the break.
Asked about Matuidi, Ancelotti said: "It's not serious, he just took a big knock."
PSG will be back at the Parc des Princes on Wednesday to take on Dinamo Zagreb in the Champions League.
There was more disappointment for champions Montpellier whose difficult start to the season continued with a 1-1 draw against strugglers Troyes, while 2011 winners Lille claimed a 2-0 win at Evian Thonon Gaillard.
Saint-Etienne stay fifth on 18 points and are behind Valenciennes on goals scored after the northern side continued their good run as they moved up to fourth with a 3-1 home win against Sochaux.
Foued Kadir opened the scoring with a free kick in the 12th minute and set up Gregory Pujol for the second 15 minutes later.
Pujol put the result beyond doubt on the hour mark, beating Simon Pouplin from close range after being set up once again by Kadir.
Sebastien Roudet scored a consolation goal two minutes later.
Lille moved up to seventh, a point behind Saint-Etienne, after a Nolan Roux header and 25-metre strike from Florent Balmont gave them a 2-0 win at Evian Thonon Gaillard.
Montpellier stay 14th on 12 points after failing to beat second-bottom Troyes.
Younes Belhanda put the champions ahead with a low cross-shot in the 19th minute, only for Fabien Camus to level five minutes before the interval.
