Far tougher challenges await PSG, which is desperate to prove it belongs among Europe's elite after failing to reach the quarterfinals in the past few seasons. To go far this time, it needs Neymar in similar form later in the competition.
The Brazil star's treble included two superb free kicks, taking his tally to 10 goals in eight games overall this season. He is back in top form, following a difficult World Cup where he stood out more for his theatrics than his match-winning ability.
"Neymar was outstanding. He was just sensational, magnificent," PSG coach Thomas Tuchel said. "You can sense that he's hungry, that he wants to make the difference and win the ball back."
Tuchel went with his strongest line-up up front with Neymar, World Cup winner Kylian Mbappe, Edinson Cavani and Angel Di Maria in a 4-2-3-1 formation. They all scored in the first half except for Mbappe, who had to wait until the 70th minute for his goal following superb approach play from Neymar.
"It wouldn't be fair just to talk about Neymar, but everything revolved around him," Red star coach Vladan Milojevic said. "He's on another level."
After losing their opening group game to Liverpool, PSG played with the kind of intensity that has sometimes been lacking against weaker teams in past seasons, where it has failed to get beyond the quarterfinals of the competition despite huge expenditure on players and wages.
"It was a really top performance because we created a lot of chances," Tuchel said. "I was most pleased with the second half because we kept going."
Also Wednesday, Napoli beat Liverpool 1-0 in the other Group C game thanks to a 90th-minute goal from Lorenzo Insigne. The Italian side tops the group with four points, one ahead of Liverpool and PSG, while Red Star has one point.
Neymar, who scored twice in the French league last weekend , opened the scoring with his first free kick after 20 minutes, using his exquisite touch to perfectly flight the ball into the left corner.
Two minutes later, he swapped passes with Mbappe and sprinted into the penalty area to meet the teenager's quick cross from the right with a powerful finish into the roof of the net.
Cavani skillfully beat two players before scoring with a deflected shot in the 37th, and Di Maria astutely guided in the fourth shortly before the break.
Neymar created the fifth in typically extravagant style.
He showed great close control to dribble to the edge of the area, and then cleverly flicked a ball over the defense. Left back Bernat read the pass and cut the ball back to give Mbappe an easy tap in.
After Mbappe missed a sitter — his second of the night — Red Star's midfielder Marko Marin rifled a shot home in the 74th.
Neymar went off to a standing ovation with about 10 minutes left, just after curling in even better free kick into the top right corner.
PSG has won nine of 10 games this season, scoring 35 goals. But the 3-2 loss at Liverpool serves as a reminder it has trouble winning the big games.
Red Star last played in the European Cup in 1991 as holders, came through four qualifying rounds to reach the group stage and drew its opener 0-0 at home to Napoli.
"We had two players who had never played in the Champions League," Milojevic said. "If this (defeat) is what it takes to make us better, it will be worth it."
Red Star's fans were officially banned from travelling for this match and the next away game, after causing trouble during its playoff at Salzburg.
Still, quite a few managed to get tickets independently and sat among PSG fans at the Parc des Princes stadium. They made their presence heard when Marin scored.
A strong police presence was in place around the stadium — with both sides reputed for having hooligan elements among their supporters.
According to reports, about 150 PSG fans tried to attack a group of Serbian fans leaving the stadium after the game. Riot police quickly intervened to split the two groups and prevent the clashes from escalating.