Andre Ayew put the home side ahead from the spot after Thiago Motta saw red, but the French champions hit back with goals from Maxwell and their Swedish striker.
PSG was reduced to 10 men after just 34 minutes when Thiago Motta was sent off for a crude foul on Mathieu Valbuena in the penalty area at Stade Velodrome. And after Andre Ayew slotted the resultant spot kick, Marseille appeared set for victory against its fierce rival.
But PSG - which had not won at Marseille since 2008 - staged a stirring comeback, with Maxwell's header on the stroke of halftime giving it hope.
And the capital club completed the turnaround after 66 minutes, with Ibrahimovic stroking home the game's second penalty to give Laurent Blanc's men an excellent victory.
PSG is now level on points with Ligue 1 table-topper Monaco, but sits second on goal difference.
PSG was unchanged from its 3-0 Champions League win over Benfica, while Jordan Ayew replaced Saber Khelifa in attack for Marseille.
Marseille made the brighter start to the match, with attacking midfielder Mathieu Valbuena forcing PSG goalkeeper Salvatore Sirigu into a smart save from his curling free kick.
Sirigu was then called on to make a double save to deny Jordan Ayew and then Valbuena, while Andre Ayew should have opened the scoring but headed Rod Fanni's near-post cross just wide.
The hosts were handed a golden opportunity to seize the advantage just before the half-hour mark though, when they won a penalty after Motta's poor challenge. The midfielder was given a straight red card for the high tackle, after he failed to deal with a ball into the box, and Andre Ayew seized the opportunity, emphatically converting from 12 yards to delight the raucous home crowd.
PSG manager Laurent Blanc tinkered with his side, introducing Adrien Rabiot for Ezequiel Lavezzi in a bid to bolster its midfield, and the visitors nearly leveled proceedings shortly after when Marseille goalkeeper Steve Mandanda made an excellent save to deny Ibrahimovic.
However, Mandanda could be considered to be at fault for PSG's equalizer, as his attempt to claim Gregory van der Wiel's lofted cross was unsuccessful, with defender Maxwell beating him to the ball to head home from close range just before halftime.
PSG looked the more comfortable of the two sides in the second half, although it was fortunate not to fall behind as Sirigu stopped Dimitri Payet's effort.
Marseille failed to take full advantage of its numerical advantage and was made to pay midway through the second half when Andre Ayew was penalized for tripping Marquinhos just inside the area.
Ibrahimovic was unfazed by lazers pointed at his face from the crowd, coolly tucking his penalty into the bottom corner to give the defending champions the lead.
Marseille pressed in the closing stages to try and earn a share of the spoils, but its best effort - a header from substitute Florian Thauvin - was comfortably saved by Sirigu, as PSG held on for a gritty away win.