The Uruguayan striker pounced in the dying seconds to break Greek hearts and ensure that the Ligue 1 champions will finish top of Group CTen-man Paris Saint-Germain qualified for the Champions League knockout stages courtesy of a 2-1 win over Olympiakos on Wednesday.
The French champions will progress to the next round as Group C winners after maintaining their unbeaten start to the competition at the Parc des Princes.
PSG deservedly went ahead after just seven minutes, with Zlatan Ibrahimovic marking his 100th Champions League appearance with a clinical close-range finish.
The hosts were reduced to 10 men when Marco Verratti was booked for a second time early in the second half and the Greek side thought they had gained a point when Kostas Manolas levelled 10 minutes from time.
However, Edinson Cavani grabbed the winner in the final minute, slotting past Roberto Jimenez to secure Laurent Blanc's men the win.
Alex retained his place alongside Thiago Silva in the centre of defence for PSG, while Cavani, Maxwell and Gregory van der Wiel all returned to the starting XI after being rested for the 3-0 win against Reims.
Jeremy Menez and Lucas Moura had to be content with spots on the bench, despite both scoring at the Stade Auguste Delaune II on Saturday.
Dimitris Siovas returned from a knee injury for Olympiakos, while Konstantinos Mitroglou was named in the starting XI, having been rested for Saturday's 4-1 win over Panthrakikos, as he looked to add to his 17 goals this season in all competitions.
The Ligue 1 leaders were ahead after seven minutes courtesy of Ibrahimovic, as he equalled the record amount of goals in a Champions League group stage with his eighth of the campaign.
The ball was spread wide to Van der Wiel on the right, who crossed for the Sweden international to sidefoot into the roof of the net.
Buoyed by their early opener, PSG dominated possession but struggled to create further chances, while Mitroglou got on the end of a Joel Campbell ball to force a smart stop from Salvatore Sirigu.
PSG almost doubled their lead after half an hour when Maxwell's cutback from the left by-line evaded Cavani inside the area.
Mitroglou then again tested Sirigu from inside the area after fortunately finding himself through on goal following a Thiago slide tackle.
Jimenez was called on to deny Cavani's fierce effort six minutes before the break, while Ezequiel Lavezzi fired past Jimenez's left-hand post with the last chance of the half.
Verratti was shown a second yellow card within the first minute of the second half, as he was cautioned for pulling back Vladimir Weiss after his first yellow had been given for a handball after 29 minutes.
Ibrahimovic hit a vicious free-kick on target five minutes later before Jose Holebas attempted to replicate him at the other end - only for his long-range effort to fly harmlessly over Sirigu's crossbar.
Jimenez was called on to deny substitute Adrien Rabiot 18 minutes from time, getting down well to his left and tipping the strike wide.
Manolas was on hand to bury a loose ball in the area after Sirigu had parried an Alejandro Dominguez header, but it was not enough as Cavani prodded home Rabiot's throughball in the 90th minute to deny Olympiakos qualification.