"They caused us some problems as we expected from Olympiakos at home. But we gained possession and Olympiakos used up a lot of their energy in the first half," PSG coach Laurent Blanc said. "Their performance fell off considerably in the second half, so we kept playing hard and we got the result.
"We fell too far back in the first half ... but closed the gap between defense and our forwards after the break. We had a lot more space in the second half."
Cheered on by 30,000 noisy fans at Karaiskaki Stadium, Olympiakos had a strong start and hit the bar twice in 15 minutes, with Weiss in the opening seconds and again with David Fuster.
But PSG withstood the early threats and waited out the hosts, with Ibrahimovic falling back and Uruguay striker Cavani posing a constant threat.
Ibrahimovic was knocked to the ground by Andreas Samaris but missed from the penalty spot in the 82nd minute, his shot saved by newly-signed Olympiakos goalkeeper Roberto Jimenez.
"The score made it look like Paris Saint-Germain had an easy win, but that wasn't the case. To lose this way and with that score was tough for us." Olympiakos coach Michel Gonzalez said.
Olympiakos midfielder Yiannis Maniatis said his team played an open game "but it was those three dead balls that cost us."
"We really let ourselves down," he said. "You lose control for a minute and the goals start going in against you."