Carlo Ancelotti's side went ahead at Stade Armand Cesari after just six minutes when Nene's free kick was turned across the face of the goal by Zlatan Ibrahimovic, and Jeremy Menez blasted the ball home from just yards out.
Bastia could have restored parity in the 11th minute had Salvatore Sirigu not made a good save from a Wahbi Khazri effort.
Blaise Matuidi could have made it 2-0 to the visitors on 17 minutes, and then Anthony Modeste left a half-chance to equalise for Bastia go begging.
Khazri forced Sirigu into making another important save from his free kick in the 31st minute, before Ibrahimovic's backheel from a Nene cross went narrowly wide.
The Swedish striker made amends for his earlier miss in the 40th minute when Marco Verratti delicately chipped a ball towards him and he slotted it home after getting past Magno Macedo Novaes.
Jeremy Choplin and second-half substitute Florian Thauvin went close to halving the deficit for Bastia after the restart, while Ibrahimovic almost scored his second goal of the afternoon on 69 minutes.
PSG eventually made it 3-0 in the 72nd minute when Matuidi raced past the Bastia defence and shot past Novaes.
Then in the final minute of normal time, Ibrahimovic found the target for the second time in Bastia after hoodwinking the hosts' defence and shooting home.