The big-spending visitors went behind in the sixth minute when Eduardo scored for the Corsicans, only for Ezequiel Lavezzi and Blaise Matuidi to find the net each side of the interval to lift PSG to 47 points from 20 games ahead of Monaco.
The only black mark for PSG was that Ibrahimovic, who has eight assists to go with 15 league goals in 19 appearances, will get a one-game ban for his third yellow card in four matches.
Second-placed principality club Monaco have 42 points after being held to a 1-1 draw at lowly Montpellier on Friday.
Ajaccio, who have only won one league game this season and are now nine points off the safety zone, went ahead when Eduardo tapped in after Benjamin Andre's fluffed effort in the area.
PSG increased the pressure but were denied by goalkeeper Guillermo Ochoa, who kept out Lavezzi from close range, while Ibrahimovic's powerful free kick hit the post on the half-hour.
However, there was nothing Ochoa could do four minutes from the break when Lavezzi slotted the ball home after collecting Ibrahimovic's back pass in the box.
Ajaccio were on the back foot but still looked dangerous on the break with PSG keeper Salvatore Sirigu tipping away Eduardo's low cross-shot in the 65th minute.
With an embarrassing draw looming, PSG manager Laurent Blanc sent on Javier Pastore and Lucas for Alex and Lavezzi in the 72nd minute, a move that paid dividends moments later.
Pastore, who has only showed glimpses of his talent since joining from Palermo in 2011, had an immediate impact as the Argentine unsettled the Ajaccio defence in the 74th with a brilliant dribble followed by a fine pass to Ibrahimovic.
The Swede headed the ball into the path of Matuidi, who sealed all three points with a diving header.
Ajaccio 1 - 2 Paris Saint Germain
Bordeaux 0 - 1 Toulouse
Guingamp 0 - 0 Saint Etienne
Lyon 2 - 0 Sochaux
Rennes 0 - 0 Nice
Valenciennes 3 - 2 Bastia
- Sports & Recreation
- Ezequiel Lavezzi
- Blaise Matuidi