Kylian Mbappe, the final member of the superstar forward trio, added a fourth before the break but it could have been many more.
He loves playing against the Scottish side and he claimed an assist as it became 3-1 just before the half-hour, using his shoulder to help an Alves ball across the face of goal for Cavani to turn in.
The match was so heavily weighted in the favour of the home side, centre-back Thiago Silva was flagged offside as he tried to latch into an outrageous lobbed pass from Neymar over the top of the visiting defence.
Rodgers had gambled on physicality to compete with the technical abilities of one of the sides considered favourites to lift the Champions League crown next June in Kyiv.
Moussa Dembele stunned the French side by netting against his former club inside two minutes.
The result all but guarantees PSG - who have won all five games - will finish ahead of Bayern Munich at the top of group B, given their massive advantage on goals difference.
In many ways, it was a odd move from the manager, who has incessantly stressed the importance of being able to retain possession at this level.
"They know their role when they have the ball, their relationship on the pitch with their teammates and how to give the best options to demonstrate their qualities as part of an attacking trio".
The best the Hoops can reasonably hope for is a place in the Europa League and they must finish above Anderlecht to play in Europe in the new year. It's a sore one, but I'm certainly not anywhere as disapponted as I was against Barcelona, funnily enough (a 7-0 defeat last season).
Celtic were thumped 7-1 by an enormous PSG team in the French capital.
Things did not get any better for the Scottish team in the second half and it was only a matter of time before PSG scored another goal. And they, of course, still have one further match to play.