PSG were without the injured Kylian Mbappe and he was replaced by Pablo Sarabia, who joined Lionel Messi and Neymar in a three-pronged attack while midfielder Vitinha made his debut for the champions.
The visitors clicked into gear from the word go as Neymar gave them the lead in the ninth minute with a strike into the bottom corner after a flicked pass by Messi from Sarabia's cross.
The Parisians continued to threaten and Achraf Hakimi doubled their lead on 26 minutes with looping strike into the roof of the net after he burst through in the box from Neymar's pass following a counter-attack.
PSG went out of sight in the closing phase of the first stanza from a set-piece after Marquinhos made a late run and guided home a close-range header from Neymar's delivery.
Clermont had a promising start in the second stanza after Komnen Andric came close to pulling a goal back with a strike from a turn on the edge of the box that missed the top corner by a whisker.
However, PSG regained control after that but they were mainly knocking the ball around without rushing forward and Galtier eventually made a double change on 67 minutes as Leandro Paredes replaced Vitinha and new signing Nordi Mukiele took the place Ramos at the back.
The visitors got their swagger back as Messi had big chance after a bouncing pass by Nuno Mendes fell kindly for him in the box but he could not find the target from close range.
However, Messi eventually made it 4-0 for PSG in the last ten minutes after he started a brilliant run, went past a couple of challenges to link up with Neymar and finished it off with a tap-in from the Brazilian's square pass.
Messi saved the best goal for last to complete his brace four minutes before time with an audacious overhead kick after he chest-trapped Paredes' lofted pass in the box.