PSG came from behind to take the lead through a Nene double, taking his season's tally to 13 goals, but Monaco grabbed the equaliser two minutes from time thanks to Daniel Niculae.
PSG lie in second place on 31 points, level with leaders Lille, who host Nancy on Sunday, and Stade Rennes, who are in third after snatching a 1-0 victory over Valenciennes.
At the Parc des Princes, Monaco made the better start thanks to a powerful header by Sebastien Puygrenier in the 32nd minute.
Nene equalised five minutes before half-time with a beautiful volley before putting his team 2-1 up shortly after the interval following neat work in Monaco's box.
PSG looked on course to victory but let their concentration wander and conceded a late goal amid confusion in the penalty area.
"It was very hard tonight but we showed a lot of solidarity and kept faith all the way", Monaco goalkeeper told French TV channel Orange sport.
PSG had also missed out on top spot in late November at Lyon when they were held to a 2-2 draw in the dying minutes.
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"MAGICAL MOMENT"
In Rennes, Jean Armel Kana Biyik scored deep in added-time from Fabien Lemoine's corner to prevail over Valenciennes.
Lemoine had come on three minutes earlier for his first appearance since August when he took a nasty blow during a match against Nancy and later had to have a kidney removed.
"It was a magical moment... one of the most beautiful days of my life", Lemoine was quoted as saying by sports daily L'Equipe's website.
"I had pins and needles in my legs. I am not used to kicking corners, but I wanted to touch the ball so much."
Despite securing only their third succes in their last 10 league matches, Rennes are still firmly in the title race.
St Etienne went fifth on 28 points thanks to their 2-0 victory over basement club Arles-Avignon.
Laurent Batlles and Emmanuel Riviere scored within the space of two minutes and condemned Arles to their 13th league defeat in 18 matches.
In Toulouse, Paulo Machado scored once in each half, the second a penalty, to help the hosts beat Lorient 3-0 and move up to eighth.
Elsewhere, Montpellier drew 1-1 with Auxerre after taking the lead through a spectacular goal by Younes Belhanda in the 58th minute.
The striker broke into Auxerre's box with a menacing run and performed a nutmeg on defender Pascal Mignot before chipping the ball past keeper Olivier Sorin.
But, after having coach Rene Girard sent off for dissent, Montpellier were pulled back when Burkina Faso midfielder Alain Traore scored in the 76th minute.
Nice were also held to a 1-1 draw against Brest despite dominating the second half. The match between Lens and Caen, both in the relegation zone, was rescheduled for Sunday because of heavy snow.
