Javier Pastore's first league goal of the season, and his first in 1,207 Ligue 1 minutes, put Laurent Blanc's side ahead but they were not able to hang on and record an eighth away win in the league this season.
Monaco battled hard and they were level with 16 minutes to go as Thiago Silva put through his own goal.
The league leaders piled on the pressure in an attempt to find a winner but their efforts proved in vain and they had to settle for a point, which also extended Monaco's unbeaten run to five league games.
The draw means the gap at the summit remains at five points, with both games between the two sides having ended all square this season.
PSG, who recalled goalkeeper Salvatore Sirigu, made the perfect start to the match with a goal after just eight minutes.
Lucas Moura's corner from the right was met by Alex inside the penalty area and his header looped off a defender towards the back post, where Pastore was on hand to turn the ball home from close range.
Rather than panic after going behind so early, the hosts attacked the league leaders and Emmanuel Riviere had two chances in as many minutes to level.
The first came after Sirigu had made an excellent save from Lucas Ocampos as the loose ball dropped to the striker, but he was unable to guide his shot towards the open goal, instead firing wide.
Then, a few moments later, the 23-year-old Riviere wriggled free inside the penalty area only for Thiago Silva to deny him with a perfectly timed challenge.
Zlatan Ibrahimovic's first sight of goal came in the 16th minute, but he failed to get enough on a Blaise Matuidi cross, and seven minutes later his swerving free-kick was pushed wide by Danijel Subasic.
Pastore should have doubled his tally, and his side’s advantage, just after the half-hour mark when he was superbly found by Marco Verratti. The 24-year-old jinked past Eric Abidal but rather than find Ibrahimovic, he went for goal and fired wide.
Ibrahimovic's personal battle with Subasic continued in the second half, with the goalkeeper again coming out on top as he got down well to push the Sweden international's free-kick wide of goal in the 54th minute.
The introduction of Dimitar Berbatov just after the hour for Valere Germain gave the hosts more of an attacking threat in the final third, and within 10 minutes of that change Monaco were level.
Having survived a spell of PSG pressure, Monaco finally had time on the ball inside the opposition half and when Joao Moutinho released Fabinho, the Brazilian full-back delivered a low cross into the penalty area that was diverted into his own goal by Thiago Silva.
Both sides pushed for a late winner, but both Ibrahimovic and Fabinho were denied.
