The Sweden striker, who replaced Kevin Gameiro in the 65th minute, converted a penalty to add to Jeremy Menez's second-half opener and Ezequiel Lavezzi wrapped up victory with one minute left to put PSG on 51 points from 24 games.
Keeper Salvatore Sirigu failed to chalk up his ninth consecutive clean sheet in the league as Wahbi Khazri scored 13th-placed Bastia's consolation goal with a 35-metre free-kick.
"All the games are difficult especially at the Parc des Princes where our opponents come to defend," midfielder Blaise Matuidi told BeIN Sport television.
"It is going to be a long season and that is why the coach let some players rest a little bit with Tuesday's big game in mind," added substitute Matuidi, referring to next week's Champions League tie with Valencia.
With Ibrahimovic and Lavezzi also starting on the bench, PSG were quiet up front early on. Brazilian Lucas failed to threaten in attack and the home side were booed off by an angry crowd at half-time.
Gameiro, who hit the woodwork midway through the first half, came close again after the break when Mickael Landreau stretched to his left to tip away the France international's backheel.
Menez found the back of the net 11 minutes into the second half with a low shot from 18 metres that slipped under Landreau's right arm.
Ibrahimovic quickly found his stride when he came on, triggering chants from the fans with a series of spectacular dribbles in the box.
In the 71st minute he beat Landreau from the spot after Lucas was fouled by Julian Palmieri.
Bastia were lucky to escape when referee Olivier Thual did not show Samba Yatabare a second yellow card for a foul on Menez.
Substitute Khazri then pulled one back for the visitors when he lobbed Sirigu in the 83rd minute, taking advantage with the Italian keeper out of position as he tried to organise his defence.
Khazri looked set to double his tally when he dribbled the ball past Sirigu, only for his low shot to be blocked by defender Gregory van der Wiel.
Lavezzi, who had replaced Lucas, put the game beyond Bastia's reach by poking the ball in after a Menez cross was deflected into his path.
