PSG, who suffered a shock 4-2 defeat in the same fixture last season, were unconvincing during the first half, but their all-time top scorer Ibrahimovic struck a double to settle the match after the break.
His first arrived in the 72nd minute when he met a cross by Edinson Cavani and fired past Jean-Louis Leca and he doubled PSG's advantage 11 minutes later with a deft finish to convert an excellent cross from Serge Aurier.
Laurent Blanc's side, perhaps distracted by the upcoming Champions League visit of Real Madrid, were far from their best though and the coach's selection was clearly affected by a costly international break.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
PSG travelled to Bastia without the likes of Marco Verratti, David Luiz, Kevin Trapp, Angel Di Maria and Blaise Matuidi due to injury and suspension, and their performance was unconvincing during the opening 45 minutes.
"I am very satisfied with the three points, and they allow us to prepare well for Madrid," Blanc said.
"Our preparation conditions weren't ideal with players coming back (from the international break) very late and having made senseless long trips. I wanted to preserve my players by rotating a lot."
The French champions have 26 points after 10matches, having won eight and drawn two so far this term.
Second-placed Angers continued their superb and unexpected run by beating Toulouse 2-1 away from home.
The newly-promoted side are level on points with Caen in third, who beat Reims 1-0 away thanks to a late goal from Julien Feret.
Elsewhere, Nantes beat Troyes 3-0, Lille drew 1-1 away at Guingamp and Saint-Etienne overcame bottom club Gazelec Ajaccio 2-0 at the Stade Geoffroy-Guichard to move into fourth place.
(Writing by Ed Dove, Editing by Martyn Herman)
