Ibrahimovic swept in a cross from Gregory van der Wiel in the 7th minute to get his eighth goal of the competition and set a new single-season club record. Manolas tapped in after 'keeper Salvatore Sirigu saved an Alejandro Dominguez attempt.
"I have the impression that when we equalized, PSG really wanted the game to finish and were waiting for the whistle," Olympiakos coach Michel said. "We have one game left against Anderlecht and if you look at the five games I think we deserve to qualify."
PSG drew 1-1 with Anderlecht in its previous game and again looked vulnerable to counterattacks even before Verratti's red card.
"I think we respected PSG too much," Michel said. "We saw that we could get into their penalty area very quickly and we just needed to show more audacity."
Verratti had only himself to blame after the first yellow was needless a blatant handball to stop an Olympiakos attack from midfield and the second was careless as he tugged back David Fuster's shirt.
"Marco deserved the first yellow. It's stupid but sometimes you don't really think about things because you're doing it to break up a move, to help the team," Blanc said. "He put us in difficulty, but I don't hold it against him."
PSG started the game at its usual frenetic pace.
Fullback Gregory van der Wiel was given far too much space down the right and delivered a perfect cross for Ibrahimovic, who thumped the ball into the roof of the net from the edge of the box to break George Weah's single-season club record of seven.
"I'm lucky enough to have two great players who can score goals," Blanc said. "Great scorers like that always show up for big games."
But Blanc warned his players before the match about casual defending and Olympiakos went close to equalizing two minutes later, when Joel Campbell tried his luck with a low shot that forced a smart save from Sirigu.
Van der Wiel was getting behind the Olympiakos defense with ease and almost found Ibrahimovic again moments later, but the shaky defense hacked the ball clear.
"We were much better than them in the first half but then we made things difficult for ourselves," midfielder Thiago Motta said. "We also won with our hearts, it's important to show such character."
Kostas Mitroglou the hero of Greece's World Cup playoff win against Romania prompted another good Sirigu save in the 34th. Campbell then headed over from a free kick as the visitors enjoyed a decent spell of pressure.
Despite being a player down, PSG pushed forward and earned a free kick about 35 yards from goal. Ibrahimovic hit a fierce, swerving shot and Jiminez flung himself to the right to make an excellent save.
"It's the second time (this season) we've won with 10 against 11," Blanc said. "It can serve us well in the latter stages of the competition."
Moments after Ibrahimovic was substituted, Olympiakos forced a corner. Manolas's header bounced off Rodriguez's leg and toward goal, drawing a fine reflex save from Sirigu but he was helpless to stop Manolas getting to the rebound.
Olympiakos' only other defeat of the season was a 4-1 loss to PSG and the Greeks head into the final Group C game level on points with Benfica after the Portuguese side won 3-2 at last-place Anderlecht.
