Layvin Kurzawa's opener for the visitors after the break was cancelled out by Montpellier's on-loan AC Milan forward M'Baye Niang, who followed up to score on his league debut after his penalty was saved by Danijel Subasic midway through the half.
Monaco stayed second in the standings with 42 points from 20 games, two points behind PSG who travel to bottom club AC Ajaccio on Saturday (1600 GMT).
Montpellier, the 2012 champions, remained one place above the relegation zone in 17th with 18 points and are now four points clear of the bottom three.
"we can't be satisfied as we wanted all three points but we knew Montpellier would be aggressive," Monaco midielder Joao Mountinho told BeIN Sport.
"Let's focus on keeping that second place for now but we still have the title in the back of our minds."
Monaco lead third-placed Lille, who host Stade Reims on Sunday, by two points.
After a dull opening half, Monaco went ahead when fullback Kurzawa headed home from James Rodriguez's free kick.
But Eric Abidal, again the weak spot in the Monaco defence, brought down Remy Cabella in the area in the 67th minute.
Although Subasic parried 19-year-old Niang's penalty, the striker tapped in the rebound to earn a share of the points.