PSG opened the scoring early at the Parc des Princes through Zlatan Ibrahimovic, only for Radamel Falcao to level for the leaders later in the first half.
Ibrahimovic got in front of Danijel Subasic to meet a left-wing cross from Maxwell and poked the ball into the back of the net, but Laurent Blanc's side were dealt a blow when captain Thiago Silva limped off with a hamstring injury.
And things got worse for them soon after when Falcao grabbed an equaliser for the visitors. The Colombian striker struck in the 20th minute, getting to a Joao Moutinho cross at the front post and bundling the ball over the line.
Chances were at a premium in the second half as both sides pushed for the win, with PSG coming closest to taking all three points through an audacious Ibrahimovic backheel.
However, Blanc and his Monaco counterpart Claudio Ranieri were forced to settle for a draw that maintains both teams' unbeaten starts to the season.
Elsewhere, Lyon ended a run of four games without a win with a 3-1 victory over Nantes at the Stade Gerland, but they had to come from behind to take the points after Jordan Veretout gave the visitors the lead.
Bafetimbi Gomis equalised for the hosts with his first goal of the season, the striker linking well with Jimmy Briand before firing beyond Remy Riou.
Clement Grenier then gave Lyon the lead in the 55th minute with a perfectly placed free-kick, before Briand sealed the points with a close range header.
Nice continued their strong start to the season with a convincing 4-0 win over second-bottom Valenciennes.
Dario Cvitanich opened the scoring from the penalty spot for Calude Puel's side in the 32nd minute after Benjamin Angoua had handled, and Eric Bautheac doubled their advantage just before the break.
Christian Bruls and Alexy Bosetti then scored within the space of five second-half minutes to secure victory and condemn their opponents to a fifth successive defeat.
In Sunday's other fixture, Lorient had to come from behind on two occasions to take a point against Bordeaux as the sides shared six goals at the Stade Yves Allainmat.
Having lost their last three matches in all competitions, things started well for the visitors as Cheick Diabate opened the scoring from the penalty spot.
Vincent Aboubakar - who gave away the penalty - equalised midway through the half, only for Gregory Sertic to put Bordeaux back in front a minute later with a long-range effort.
Henri Saivet then made it 3-1 on the half hour mark, but Lorient fought back well, with Kevin Monnet-Pacquet and Sadio Diallo striking in the 44th and 58th minutes respectively to give them a hard-earned point.
