The match got off to a slow start, with the only half-chance in the opening exchanges coming when Thiago Silva volleyed a first-time effort over the crossbar having been left unmarked at the back post.
Alphonse Areola in the PSG goal wasn't called into action until shortly before the half-hour mark, but his first stop was an unconvincing one as he reacted late to turn Stevan Jovetic's long-range free kick over the crossbar.
Jovetic continued to look like Inter's most dangerous player, and after dragging one effort a couple of yards wide he found himself with another clear chance when the ball dropped kindly for him inside the area, but his well-struck shot hit the head of Silva and went over.
PSG responded with a chance of their own moments later when Andrea Ranocchia unfathomably ducked under a lofted ball into the box to leave Maxwell with only the keeper to beat, but the full-back lifted his finish over the top.
Aurier was the French champions' most dangerous attacker on the night, though, and he almost doubled his personal tally just before half time when Ben Arfa and Lucas Moura combined to find him in the box, but this time he couldn't hit the target with his effort.
Despite PSG having the better of the first half, the two sides went into the break all square as Jovetic levelled things up from the spot in the third minute of stoppage time, placing his penalty into the top corner after Lucas had been penalised for a handball.
PSG wasted little time in looking to regain their lead in the second half, with Adrien Rabiot dragging one shot wide in the opening minute after the restart before Layvin Kurzawa failed to hit the target at the back post with most of the goal gaping.
Kevin Trapp was forced to punch away a Jovetic piledriver shortly afterwards, but the main attacking threat continued to come from PSG and Aurier almost got his second of the night when a mis-hit cross sailed over the head of Handanovic and clipped the crossbar.
Emery's side did take the lead again shortly after the hour mark, though, and once more Handanovic should have done better as he failed to keep out Kurzawa's curling free kick from 30 yards.
Kurzawa had another go moments later but this time was unable to hit the target, and Edinson Cavani's radar was also off 15 minutes from time when he curled wide having been left in space inside the area.
The third goal did arrive with just three minutes remaining, though, as Aurier wrapped up the win with his second of the night, planting a header past the keeper after Inter's defence had gone to sleep from a free kick.
PSG were able to comfortably see the game out in the closing stages, with only a smart save from Juan Pablo Carrizo preventing the Ligue 1 outfit from extending their lead further as they picked up all three points.