Edinson Cavani's late penalty had looked like sending the hosts to within one point of the summit, but Bernardo Silva struck at the death to ensure that Monaco got the point they needed to jump back above Nice.
The first chance of the match fell the way of PSG after 11 minutes when Cavani found space to shoot, but he couldn't keep his effort down as it flashed narrowly over the crossbar.
Monaco soon responded, though, and after Thomas Lemar fired a free kick wide it took a fingertip save from Kevin Trapp to keep Europe's highest scorers at bay when he pushed Fabinho's dangerous strike over the top.
The title hopefuls continued to go toe to toe with each other, and it was the champions who were the next to come close when Cavani's header forced a save from Danijel Subasic.
Marquinhos then put one over the crossbar on the half-hour mark, but it was Cavani who continued to look the most likely for the home side and he should have done better five minutes later when he seemed to misjudge a Layvin Kurzawa delivery into the area.
PSG almost broke the deadlock with just three minutes remaining until half time when Lucas Moura and Cavani both had chances in quick succession, but Subasic pulled off a double save to keep the match goalless.
Having held on until the break, Monaco almost made a perfect start to the second half when Radamel Falcao found himself with only the keeper to beat, but Trapp was equal to the test and made a fine reflex save to deny the striker.
The PSG shot-stopper made a more routine save to deny Lemar shortly afterwards, but he would not be able to see the game out and was forced off in the 53rd minute due to a hamstring injury.
The home side's first chance of note in the second half did not arrive until the 72nd minute when Julian Draxler rose highest in the area, only to nod his finish inches over the crossbar.
Draxler would have a telling impact with 10 minutes remaining, though, going down under the challenge of Djibril Sidibe in the area to win his side a penalty, which was duly dispatched by Cavani.
Monaco went in search of a dramatic late equaliser that would take them back to the top of the table and came close through Kylian Mbappe before Bernardo Silva levelled things up with the last meaningful action of the match to rescue a point.
Despite conceding late on, PSG's unbeaten home run now stretches to 22 matches, although they remain three points adrift of the leaders.
Monaco, meanwhile, sit level on points with Nice at the top of the table but move above their title rivals due to their vastly superior goal difference.