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The visitors started the match the brighter of the two sides, as Batshuayi twice tested PSG keeper Kevin Trapp, who stopped both efforts fairly comfortably.
PSG grew into the game after 20 minutes, as Ibrahimovic forced a good save from Mandanda with a fierce strike from inside the Marseille box, before Angel di Maria cut in from the right flank to fire narrowly wide.
The hosts were awarded their first penalty of the evening when Mandanda brought down Ibrahimovic in the box, and the Swedish international sent the Frenchman the wrong way to equalise on 41 minutes.
PSG won another penalty before half time, as Marseille defender Rolando was deemed to have handled the ball following a corner. Ibrahimovic took his second spot kick of the night, and fired past Mandanda again to give his side the lead.