The Brazilian gave PSG the lead after just two minutes at the Parc des Princes but Monaco scored two quick goals through Gelson Martins and Wissam Ben Yedder to move 2-1 ahead inside quarter of an hour.
A Fode Ballo-Touré own goal brought PSG level and Neymar restored their advantage from the penalty spot before half-time after a foul on Kylian Mbappé.
But Monaco, who also host PSG on Wednesday in a rearranged fixture, earned a point when Islam Slimani's goal was controversially awarded after it was initially ruled out for offside.
"We didn't put in our best performance but we tried. It was a good test. Monaco have a good team but we are superior and we must show it on the pitch," Neymar told Canal+.