First-half goals from Edinson Cavani and Neymar, a second-half header from Marquinhos and a late Kylian Mbappe strike were enough to send Thomas Tuchel's side into the last 16, despite Marko Gobeljic's finish 56 minutes in.
PSG took the lead nine minutes in, Mbappe bursting past Filip Stojkovic and squaring the ball for Cavani to tap in from six yards out.
374 - Edinson Cavani's goal ended Crvena Zvezda's run of 374 minutes without conceding a goal at home in European competition. Hurry. pic.twitter.com/eO0UkPUd2Q— OptaJean (@OptaJean) December 11, 2018
Red Star responded well to the setback but only good saves from Milan Borjan stopped Mbappe and Neymar from adding a second goal before the half-hour mark.
But there was no stopping Neymar from a dazzling finish five minutes before the break, the Brazil star collecting Mbappe's reverse pass, driving into the box and leaving Borjan on the ground with a dummy before firing home.
Red Star improved after half-time and deservedly got a goal back through Gobeljic, who volleyed expertly past Gianluigi Buffon at the near post, and the visitors looked to be unsettled for a time as the home fans roared their approval.
However, a fine free-kick from Angel Di Maria was powered into the net by an unmarked Marquinhos 16 minutes from time, and a clinical low strike from Mbappe in the closing seconds secured PSG's place in the next round as they ended a four-game winless run away from home in the competition.
What does it mean? PSG top and growing in strength
If the 3-2 loss to Liverpool on matchday one showed PSG's shortcomings, their form since that trip to Anfield has highlighted their developing quality under Tuchel.
A pair of comfortable victories over Red Star, two hard-fought draws with Napoli and a revenge win over Liverpool have all suggested this is a team adjusting to the system and demands of their head coach.
Crucially, of course, their latest victory in Serbia means they progress as group winners, giving them a better chance of a favourable draw in the next round.
Verratti in command as PSG conquer
Red Star had gone 32 games at home without defeat at Rajko Mitic Stadium until PSG's visit, but they have rarely had to deal with a midfielder in the same form as Marco Verratti, who dictated the match from start to finish in combative, elegant style.
Stojkovic left stumbling
Stojkovic would have been a little red-faced after Mbappe raced past him for PSG's first goal, and he never quite got to grips with the fluidity of the visitors' attack, even if they were not quite at their best.
Key Opta Facts
- Paris Saint-Germain have reached the Champions League knockout stages for the seventh successive season.
- PSG have scored 70 goals in all competitions this season, more than any other team in Europe's big five leagues (Man City next on 66).
- Red Star conceded as many goals in this match against PSG as they had done in their previous 14 European home matches.
- Edinson Cavani made his 50th Champions League appearance for Paris Saint-Germain – the first player to reach the milestone for the French club.
- Kylian Mbappe has been directly involved in 14 goals in his 12 Champions League group stage appearances for PSG (7 goals, 7 assists).
- Since his arrival, Neymar has had a hand in 16 goals in 13 Champions League games for Paris Saint-Germain (11 goals, 5 assists) - that is more than any other PSG player.
Before PSG find out their last-16 opponents in Europe, they travel to Dijon for a Ligue 1 clash on Saturday. Red Star, whose European campaign is over for this season, take on Cukaricki in the top flight on the same day.