Neymar's brilliant treble, which saw him draw level with Kaka as the top-scoring Brazilian in the competition's history on 30 goals, was added to by Edinson Cavani, Angel Di Maria and Kylian Mbappe.
Marko Marin got a consolation for the visitors, but it counted for little as they suffered a comprehensive defeat to Thomas Tuchel's side.
Goalkeeper Milan Borjan thwarted Mbappe at his near post as PSG started strongly, but he could do nothing to stop Neymar's superbly flighted free-kick from nestling in the bottom-left corner 20 minutes in.
Mbappe turned provider for Neymar's second barely 90 seconds later, collecting the Brazilian's throughball before squaring a low pass that was prodded high into the net by PSG's number 10.
Red Star appeared resigned to their fate and any lingering hope of a comeback seemed to be extinguished after 37 minutes, when Cavani turned into space in the box and sent a deflected strike past Borjan.
Mbappe missed an excellent chance for a fourth but Di Maria made no mistake shortly before half-time, flicking home after escaping the whole of the Red Star defence to meet Thomas Meunier's cross.
Borjan made four good saves to deny Mbappe and Neymar early in the second half and keep the scoreline reasonably respectable, and Red Star at last managed to test Alphonse Areola through Marin and Milan Rodic.
Mbappe finally got on the scoresheet, tapping in from point-blank range after Juan Bernat's cross deflected into his path, before Neymar capped a spectacular display with a stunning second free-kick to seal his hat-trick after Marin had blasted home a sliver of consolation.
What it means: PSG back on track and building momentum under Tuchel
As frustrating as the loss to Liverpool was on matchday one, PSG could point to the fact they are still developing an identity under Tuchel. It is a style that shone through against Red Star.
The movement in attack, the persistent chances created and the speed at which they pressed to win back the ball left Red Star with absolutely no answer.
Napoli will present a far greater test three weeks from now, but a repeat of this performance will put PSG firmly on track for the last 16. Red Star, though, simply have to improve to have any hope of staying alive in Europe.
Neymar dazzles in free role
Neymar has often been used as a number 10 under Tuchel, but this was arguably his best performance for some time in a PSG shirt.
His two free-kick goals were magnificent and his improvised finish from Mbappe's pass clever, but he was an all-round menace to a Red Star defence that did not know how to stop him.
Rodic left reeling
Nobody bar Borjan had a game worth remembering for the visitors, but left-back Milan Rodic will certainly not want to relive his display.
Rodic was given a torrid time by the pace of Mbappe and the trickery of Neymar, and he allowed Meunier to cross for Di Maria's goal without anywhere near enough pressure on the ball.
Key Opta stats:
- PSG have scored in each of their last 18 Champions League games; the longest current run in the competition.
- PSG have won by four+ goals on five occasions in the Champions League since the start of last season; more than any other side in the competition.
- PSG’s Kylian Mbappé has been directly involved in 16 goals in his 16 Champions League starts (12 goals, 4 assists).
Red Star have four more domestic games before they travel to Anfield in three weeks' time to take on Liverpool.