Ibrahimovic, who is three clear at the top of the league scorers table on seven goals, set up Jeremy Menez for the opener in the sixth minute then doubled the lead from close range five minutes before the break.
The Sweden frontman, who has scored in all of PSG's games he has played this season but one, wrapped up the victory in the 90th minute after Blaise Matuidi had netted the third in the 72nd.
"When the team is good, I'm doing good," Ibrahimovic, who also scored a goal in the Champions League 4-1 opening success against Dynamo Kiev on Tuesday, told French TV channel Canal+.
Unbeaten PSG are on 12 points from six games, three behind leaders Marseille, as they recorded their third successive league win while Bastia are 13th on six after suffering their fourth defeat in a row.
PSG made a perfect start, patiently controlling their hosts then going in front with their first chance when Menez tapped the ball into an empty net from Ibrahimovic's pass following a free-kick.
Bastia only threatened PSG's goal when former Paris midfielder Jerome Rothen curled a superb free-kick on target, only to see Italian keeper Salvatore Sirigu save the attempt.
The Qatari-backed club made it 2-0 when Italian prospect Marco Verratti chipped the ball over the defence for Ibrahimovic to poke past keeper Novaes.
The hosts tried to mount a challenge after the break but PSG's defence, marshalled by a classy Thiago Silva on his Ligue 1 debut, offered Bastia few goal chances.
Blaise Matuidi added a third from a neat Nene pass behind the defence and Ibrahimovic's clinical finish following another fine ball from the Brazilian winger completed their days work.
Fourth-placed Lorient could claim second spot if they beat 10th-placed Nice later on Saturday, while Toulouse take on Rennes at the same time.
On Sunday pacesetters Marseille entertain Evian while Lyon visit Lille.