After a 3-2 defeat to Liverpool in the opening round of fixtures, PSG responded with a performance of the highest quality, inspired by the Brazilian who is returning to top form after the foot injury which sidelined him for the end of last season.
Edinson Cavani, Angel di Maria and Kylian Mbappe, who with Neymar form a quartet which cost PSG over $600, were also on the scoresheet in a one-sided affair in the Parc des Princes.
Neymar laid the foundations with two first half goals in the space of two minutes, the opener a sublime free kick and then exchanging passes with French World Cup hero Mbappe before scoring the second.
Cavani netted the third on 37 minutes with the aid of a deflection before Di Maria beat Milan Borjan in the Red Star goal from a 41st minute cross by Thomas Meunier.
Neymar was involved in setting up Mbappe for his goal midway through the second half before the small contingent of Red Star fans were given some cheer by a 74th minute strike from former German international winger Marin.
Last word though inevitably went to Neymar with another curling free kick to round off his hat-trick, his 10th goal in nine Ligue 1 and Champions League games.
He was immediately substituted by Thomas Tuchel to a deserved standing ovation, the coach later describing his performance as “sensational.”
Napoli heads Group C on four points after a 90th minute goal from Lorenzo Insigne gave Napoli a 1-0 home win over Liverpool, who looked set to claim a point until the striker slid home his effort at the far post.
Messi and Rakitic shine at Wembley
Group B leader Barcelona put on a masterclass at Wembley to beat Tottenham Hotspur 4-2, the highlights a first half wonder goal from Croatian star Ivan Rakitic and a double from the magical Lionel Messi.
Barca already led from just the second minute after a blunder from returning Spurs goalkeeper Hugo Lloris allowed Philippe Coutinho to shoot into an untended net.
It was not the start a Tottenham side missing several key players wanted, with Lionel Messi tormenting them from the start.
And the second duly arrived with the ball only half-cleared before Rakitic struck home an unstoppable waist-high volley with perfect technique.
Messi hit the post twice at the start of the second half before Harry Kane gave Tottenham an unlikely lifeline with an assured finish of his own.
Messi had appeared to snuff out the comeback by finally getting the goal his performance deserved, beating Lloris after a clever dummy by Luis Suarez only for Eric Lamela to again revive home hopes with a goal from a shot which took a slight deflection.
With Tottenham pressing and coming to close to an equalizer, it was Messi again who put the game out of reach by slotting home the fourth and his second. It was his fifth goal in the campaign after just two games following his hat-trick against PSV Eindhoven.
Both Barca and Inter Milan have maximum points after two games, with Inter winning 2-1 at PSV with Mauro Icardi hitting the winner as his side recovered from a goal down.
Group A is being dominated by Atletico Madrid and Borussia Dortmund on maximum points after home wins over Club Brugge and Monaco.