PSG got off to the perfect start as Marco Verratti's ball over the top found Neymar, who calmly slotted past Lecomte for the game's opening goal after three minutes.
However, Monaco were back on level terms four minutes later as Gelson Martins managed to fire past Keylor Navas after some good work by Wissam Ben Yedder.
The visitors managed to turn things around after 13 minutes as Ben Yedder bagged a goal to go with his assist to put Monaco ahead after a lively start.
Just over ten minutes later, Monaco shot themselves in the foot when Fode Toure deflected the ball int his own net to restore matters for the defending champions.
An entertaining half was capped off with PSG being awarded a penalty three minutes before the break, which saw Neymar step up and convert the spot-kick.
After a relatively quiet start to the second half, Monaco were back on level terms in the 70th minute thanks to a strike from Algeria international Islam Slimani.
PSG coach Thomas Tuchel responded by withdrawing Angel di Maria and Verratti for Pablo Sarabia and Leandro Paredes in the final 10 minutes of the half.
However, Monaco were able to see out the closing stages of the half to secure a point at the home of defending champions.