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 went ahead after just seven minutes, with Zlatan Ibrahimovic marking his 100th Champions League appearance with a clinical close-range finish after the French side had made a bright start.
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 home past Roberto Jimenez to secure Laurent Blanc's men the win.
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 Olympiacos 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.
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 byline evaded Cavani inside the area.
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.
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 Olympiacos qualification.
