Ibrahimovic netted an early double before being replaced at halftime by Cavani who scored a superb goal just past the hour and notched a late penalty to round off a fine PSG performance.
The French champions now have 24 points from 10 games ahead of second-placed Monaco who visit Sochaux on Sunday (1200 GMT).
PSG warmed up for their third Champions League Group C game at Anderlecht on Wednesday with Ezequiel Lavezzi and Cavani on the bench and fullbacks Gregory van der Wiel and Maxwell rested.
Sweden international Ibrahimovic, however, made sure PSG did not have to sweat over the result against mid-table Bastia.
He opened the scoring in the 10th minute with a clever back heel from Lucas's cross and doubled the tally three minutes later with a header.
That put the home side in control of the game and substitute Cavani put the result beyond doubt with a sublime goal.
Starting from the edge of the area, PSG's Uruguay striker danced through the Bastia defence, dribbled past keeper Mickael Landreau and netted with a low angled shot in the 62nd.
One minute from time, Cavani got his sixth Ligue 1 goal of the season from the spot after Landreau brought down Lucas Digne in the area to move ahead of Ibrahimovic who has netted five.
In other Ligue 1 results from Saturday, third-placed Lille emerged victorious away from home with a 1-0 success at Montpellier, as did Nantes at Ajaccio.
Evian saw an early lead turned around by two late goals as they lost 2-1 at home to Guingamp, while bottom side Valenciennes took a point in a 2-2 draw at 10th-positioned Rennes.