The game got off to a fiery start when PSG's Marco Verratti and Marseille's Mathieu Valbuena got into a tussle and had to be pulled apart by their teammates.
Marseille were the first team to threaten and it took a double-save from PSG goalkeeper Salvatore Sirigu to keep out Jordan Ayew's strike and the follow-up from Valbuena.
PSG dominated possession throughout the first half but were unable to fashion any clear cut-chances.
However, Marseille were awarded a penalty as Thiago Motta was sent off for bringing down Valbuena in the box, which allowed Andre Ayew to step up and crash the ball home from the spot in the 34th minute.
The visitors grabbed their equaliser right on the stroke of half time as Gregory van der Wiel crossed towards Maxwell, who leapt to head home and leave the score at 1-1 going into the break.
PSG were awarded the crucial penalty in the second half when Ayew brought down Marquinhos, who looked to have been going nowhere in the box.
Ibrahimovic coolly slotted the spot kick past the keeper, despite the distraction of flares and firecrackers in the crowd, to give PSG a hard-fought 2-1 away win.