The champions wasted several chances in Friday's encounter at Stade Auguste Delaune as Jean-Luc Vasseur started life as Reims head coach with a surprise point.
Ibrahimovic had put Laurent Blanc's men ahead inside 10 minutes with a cool left-footed finish, but the Sweden international was also guilty of hitting the post when faced with an open goal and missing a 29th-minute penalty after he was felled in the area.
Reims made the most of the unlikely reprieve as Prince Oniangue levelled with a near-post finish from Diego's free-kick, before Antoine Devaux gave the hosts a shock lead when he slotted home from eight yards to make it 2-1 before the break.
However, Vasseur - who replaced new Lyon coach Hubert Fournier in June - was unable to celebrate a debut win as goalkeeper Johnny Placide fumbled Ibrahimovic's cross and the ball looked to cross the line before Edinson Cavani - linked with a move to Liverpool earlier in the week - made sure with the follow up.
PSG threatened early on when Cavani dragged a shot wide, but Reims failed to heed the warning and fell behind after seven minutes.
Javier Pastore easily dispossessed Odair Fortes and his incisive pass found Ibrahimovic, whose shot went through the legs of Placide.
Blanc's side then spurned two opportunities to double their advantage as Lucas Moura was foiled in his attempts to round the goalkeeper with Ibrahimovic in space, before incredibly the Swede missed an open goal - his shot hitting the post after good work from Marco Verratti.
It seemed inevitable Ibrahimovic would add to his tally when the 32-year-old went to ground in the area following Mickael Tacalfred's clumsy challenge, but his resulting spot-kick was saved by Placide.
Reims punished that profligacy and equalised against the run of play in the 22nd minute as Diego's teasing free-kick from the left was guided home by Oniangue at the near post.
Incredibly, the hosts then moved ahead 12 minutes later.
Devaux cut inside from the right to find Gaetan Charbonnier and he returned the pass back to the onrushing midfielder who calmly slotted under Salvatore Sirigu.
PSG dominated possession in the early throes of the second half, but it took until the 63rd minute for the equaliser to arrive.
Placide slapped Ibrahimovic's chipped cross from the left towards goal and the ball appeared to cross the line despite the goalkeeper's best efforts, Cavani making sure by tapping in.
Buoyed by the leveller, the visitors pushed for a winner but were twice denied in time added on by clearances off the line from Aissa Mandi as PSG had to settle for a frustrating draw.
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