The Brazil forward scored twice in quick succession to give PSG the lead at Parc des Princes and, after further goals from Edinson Cavani, Angel Di Maria and Kylian Mbappe, Neymar completed his hat-trick in the 81st minute with a second stunning free-kick of the game.
Victory put PSG back on track in Champions League Group C after they were beaten 3-2 by Liverpool in their opener, and Neymar hailed the team's performance after he took his goal tally to six in his last three matches across all competitions.
"We have played [the] better football," he said. "We showed desire to win and played our football to win the game.
"We knew it would be tough but we played at a higher tempo with a high desire to win, and finally we won the game."
Napoli are next up for Thomas Tuchel's side in Europe and Neymar indicated that anyone taking on the French champions will face a side at their peak.
Asked whether the performance against Red Star was the best of the season, he said: "Yeah, it was so far.
"Not just my best game but also from our team.
"It's not important whether I score or not. I just want my team to win, although when I score I become even happier."