Laurent Blanc's side had won six home games in a row in all competitions before the visit of Rolland Courbis' men, but that run was ended in a frustrating encounter on Saturday.
PSG suffered their first league defeat of the season at Guingamp last weekend and they dropped points again as Montpellier deservedly claimed a share of the spoils.
Talismanic striker Zlatan Ibrahimovic looked off the pace and the Ligue 1 champions lacked a cutting edge as they moved level on points with Marseille, but failed to claim the victory they needed to go top.
Thiago Silva had a header cleared off the line as PSG attempted to move up a gear in the second half, but they did not do enough to secure all three points.
Marseille have the chance to move three points ahead of PSG if they beat Lille on Sunday, while a point for Montpellier ensured they are unbeaten in their last three games.
Ibrahimovic returned to the PSG starting line-up after sitting out the Coupe de la Ligue win at Ajaccio in midweek.
PSG were soon on the front foot and the visitors were indebted to a crucial intervention from Abdelhamid El Kaoutari to deny Edinson Cavani a tap-in when Lucas Moura burst into the penalty area and fired a dangerous ball in from the left.
Montpellier also posed a threat going forward and Morgan Sanson had the ball in the back of the net after 15 minutes when he converted Anthony Mounier's cross, but the latter was adjudged to be offside.
The champions looked disjointed and Silva had to be alert to clear when Daniel Congre was left unmarked and headed the ball back across goal.
Cavani's touch let him down when Marco Verratti laid the ball off to the Uruguay striker with a deft first-time pass six minutes from half-time as PSG's frustration mounted.
El Kaoutari spared Jonathan Ligali's blushes with a last-ditch tackle to thwart Cavani after the Montpellier goalkeeper had spilled a dipping long-range free-kick from David Luiz eight minutes into the second half.
Lucas was causing all sorts of problems on the right flank and the Brazilian's inviting cross flashed across the face of goal as PSG attempted to raise the tempo.
PSG appealed for a penalty when El Kaoutari challenged Lucas, but referee Sebastien Moreira correctly pointed for a corner as the defender got a touch on the ball and Silva's towering header was cleared off the line by Mounier from the resulting set-piece.
Cavani and Blaise Matuidi were replaced by Adrien Rabiot and Jean-Christophe Bahebeck 25 minute from time after ineffective displays.
Rabiot went down under a challenge from Mathieu Deplagne four minutes from time, but referee Moreira saw nothing untoward and PSG were unable to fashion a late winner to end the year on a flat note.
