A potentially tricky opener to Group C turned out to be anything but as the visitors ran riot after the break, two Thiago Motta headers in quick succession taking the score from 1-1 to 3-1.
Marquinhos headed a fourth late on, minutes after Zlatan Ibrahimovic had had a penalty saved by Roberto Jimenez, without whom the Greeks would have been facing up to a much heavier defeat.
The hosts had been very much in the contest at the break, Vladimir Weiss having cancelled out Edinson Cavani's opener for the visitors, but they were simply blown away in the second period.
The win sent PSG top of the group, level on points with Benfica, who enjoyed a 2-0 home win over Anderlecht.
The Greeks almost hit the front after 16 minutes, but David Fuster's 25-yard volley crashed off the bar.
Instead the deadlock was broken four minutes later at the other end as Maxwell slid the ball in to Cavani, who scored with a low close-range finish.
Kostas Mitroglou headed wide as the hosts looked to respond and they drew level in the 25th minute thanks to Weiss' shot from inside the area.
PSG came out firing for the second half and might have gone back in front only three minutes in had Dimitrios Siovas not blocked Marco Verratti's effort from deep inside the area.
Cavani then forced a diving save from Jimenez, the goalkeeper turning the Argentinian's drilled effort round a post.
Jimenez produced another athletic stop to deny Gregory van der Wiel before the French side finally made their dominance count in the 68th minute.
Ezequiel Lavezzi, introduced at the break in place of Lucas Moura, swung in a corner from the left and Thiago Motta glanced home a header at the near post.
The two combined again four minutes later, Thiago Motta this time meeting his team-mate's delivery in the centre of the area and sending another header low into the net.
The French side were rampant now, with seemingly only Jimenez doing anything to keep them out.
He parried a Cavani curler from the edge of the area before turning away an Ibrahimovic penalty in the 81st minute, awarded following a foul on the Swede by Andreas Samaris.
But he could not prevent the visitors getting a fourth four minutes from time, this time Thiago Motta providing the corner from which Marquinhos headed home.