Elsewhere, substitute Kevin Monnet-Paquet equalised with a minute to go to earn fourth-placed Lorient a 1-1 home draw with mid-table Nice while Toulouse goalkeeper Ali Ahamada netted with a stoppage-time header in a 2-2 home draw with Stade Rennes.
Ibrahimovic, three clear at the top of the league scorers chart with seven goals, set up Jeremy Menez for PSG's opener in the sixth minute before making it 2-0 for the visitors from close range five minutes before the break.
The Sweden striker, who has scored in all bar one of the PSG games he has played this season, was also on target in the 90th minute after Blaise Matuidi had netted the third midway through the second half.
"When the team does well, I do well," Ibrahimovic told the Canal+ television channel.
It was unbeaten PSG's third successive league win. Bastia are down in 14th place after suffering their fourth defeat in a row.
At Lorient, Camel Meriem volleyed Nice in front after 40 minutes when the home defence failed to clear.
The hosts, who were reduced to nine men at Stade Rennes last weekend, had defender Gregory Bourillon sent off for elbowing Dario Cvitanich in the 66th minute but Monnet-Paquet levelled for Lorient after a fine solo run in the 89th.
STRONG RUN
Promoted Reims continued their strong recent run as they defeated lowly Nancy 2-0 to rise to fifth place with 10 points.
Gaaetan Courtet headed home a corner in the seventh minute and Diego doubled the lead with a penalty in the second half.
PSG made the perfect start at Bastia, going in front with their first chance when Menez tapped the ball into an empty net from a pass by Ibrahimovic.
Bastia went close when former PSG midfielder Jerome Rothen had a curling free-kick well saved by Italian keeper Salvatore Sirigu.
The visitors made it 2-0 when Italian prospect Marco Verratti chipped over the defence for Ibrahimovic to poke the ball home.
Bastia tried to rally but PSG's defence, well marshalled by Thiago Silva on his Ligue 1 debut, offered them few openings.
Matuidi added the third goal following a neat pass over the defence by Nene and Ibrahimovic completed the victory with a clinical finish following more good work by the Brazilian winger.
Struggling Sochaux clinched a second successive 3-1 victory, at home to promoted Troyes who are bottom of the table without a win.
