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.
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.
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.
