Laurent Blanc's side had opened their Ligue 1 camapign with a frustrating draw away to the same opponents, but saw any hopes of a quadruple of titles go out the window courtesy of a 2-1 home defeat.
They dominated the early proceedings, as Lucas Digne had a goal disallowed for offside, while Blaise Matuidi also spurned a golden opportunity.
Montpellier took the lead completely against the run of play, as a goalkeeping blunder from Nicolas Douchez saw Daniel Congre head into an open net in the 20th minute.
Digne squared for an Edinson Cavani equaliser 10 minutes later, but the match was decided by Victor Montano's bullet header from a corner in the 69th minute.
Monaco's 3-0 win at Monts d'Or Azergues was soured by a knee injury suffered by star striker Falcao.
Falcao was forced off on a stretcher and while the severity of his injury is unknown, it took the gloss off the win.
The Colombian forward opened the scoring in the 29th minute before Emmanuel Riviere added a second-half double for Claudio Ranieri's side.
Fifth-tier Fa Ile Rousse Monticello produced a shock, edging out top-flight Bordeaux 4-3 in a penalty shootout.
No goals were scored in normal time or extra time, forcing penalties, and Ludovic Sane missed the crucial spot-kick for Bordeaux, who sit ninth in Ligue 1.
Moulins, who play in the fourth tier, also produced a memorable win, coming from behind to beat Ligue 1 Toulouse 2-1.
Eden Ben Basat gave Toulouse the lead in the 31st minute, but a second-half double from Sebastien Da Silva gave the hosts victory.
Lyon avoided a shock of their own against Yzeure of the fourth division, as they won 3-1 on the road.
Lamine M'Baye put Yzeure in the lead with 15 minutes left, but Jimmy Briand, Yoann Gourcuff and Steed Malbranque netted in response for the victors.
