David Luiz, Thiago Silva and Lucas Digne all came close for the French champions but the visitors ultimately held on with relative ease to claim a surprise point.Paris Saint-Germain missed the chance to go on top of Ligue 1 after being held to a disappointing 0-0 draw at home against Monptellier.
Laurent Blanc's men had been hoping to move two points clear of title rival Olympique de Marseille with a win at the Parc des Princes, but they struggled to creat any clear-cut chances during a dismal first-half showing.
David Luiz tested Jonathan Ligali shortly after the restart, Thiago Silva had a header cleared off the line, while Lucas Digne came close to a last-minute winner, but Montpellier held on with relative ease to claim a surprise point.
PSG suffered its first Ligue 1 defeat of the season last weekend, at Guingamp, but the French champions had won six home games in a row in all competitions before the visit of Montpellier.
However, 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. Marcelo Bielsa's men now have the chance to move three points clear if they beat Lille on Sunday.
Ibrahimovic returned to the PSG starting lineup after sitting out the Coupe de la Ligue win at Ajaccio midweek.
The hosts 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 ruled 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 halftime as PSG's frustration mounted.
El Kaoutari spared 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 was unable to fashion a late winner to end the year on a flat note.