Laurent Blanc's men had won six home games in a row in all competitions before playing host to Rolland Courbis' side on Saturday, but that run was ended in a frustrating contest.
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 was far from his best and the Ligue 1 champions lacked 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.
Monaco, meanwhile, head into 2015 on the back of four successive Ligue 1 wins after they snatched a late 1-0 triumph at lowly Metz.
The two sides looked destined to play out a goalless stalemate, but Yannick Ferreira Carrasco latched on to Lacina's Traore's delivery and fired home with 11 minutes to go, propelling Monaco above Bordeaux, who are in action against Lyon on Sunday.
Rennes suffered a third consecutive league defeat as they were beaten 3-1 at home by Reims despite taking a first-half lead, allowing Nantes to move above them and on to 30 points thanks to a 2-1 win at Lorient.
Rock-bottom Caen avoided suffering a fourth successive defeat as they claimed a 1-1 draw at home against fellow strugglers Bastia, who remain in 19th place, while Guingamp and Toulouse also drew by the scoreline.
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