If league leader Paris Saint-Germain wins at fifth-place Nantes on Sunday it will move 11 points clear of Monaco with 20 of 38 matches played.
Monaco scored more than 150 goals in all competitions last season, finishing eight points ahead of PSG in Ligue 1, plus reached the Champions League semifinals.
But Monaco sold four key players in the offseason and was toothless against the best defense in France, especially without rested top scorer Radamel Falcao.
Eighth-place Montpellier has conceded only 13 goals in 20 league games - two less than PSG - and it showed as Monaco failed to muster clear chances.
Monaco will drop to third if Lyon beats Angers at home on Saturday.
Next up for Monaco, meanwhile, is a French Riviera derby at home to Nice on Tuesday.
Nice is in sixth place after scraping a 1-0 home win against Amiens, with midfielder Pierre Lees-Melou scoring with a deflected effort midway through the second half.
THAUVIN MAKES HIS MARK
Winger Florian Thauvin joined PSG's Neymar as the best passer in the league and added a goal as fourth-place Marseille won at Rennes 3-0.
He almost got an incredible fourth goal for Marseille in injury time, hitting the crossbar with a delightful floating chip from near the halfway line.
Thauvin has nine assists, in addition to nine league goals, and is staking a strong claim for a place in France's squad for the World Cup in Russia. More scintillating performances like this and it will be easy for coach Didier Deschamps to make up his mind.
After shrugging off missing a first-half penalty, Thauvin set up striker Valere Germain for a close-range finish in the 35th minute.
Midfielder Morgan Sanson made it 2-0 with a fine curling strike from the edge of the penalty area just before halftime, after swapping passes with Germain.
The irrepressible Thauvin finished off Rennes in the 82nd, drifting to the back post to meet Luiz Gustavo's dipping cross and sending a looping header over goalkeeper Tomas Koubek.
"We won in style," Thauvin said. "I hope we can keep going like this."
Koubek and Marseille counterpart Steve Mandanda did well in the first half, with Koubek clawing away Thauvin's penalty with both hands in the 27th minute.
Under-pressure Bordeaux coach Jocelyn Gourvennec's decision to hand striker Gaetan Laborde his first start of the season paid off.
Laborde previously made only five substitute appearances this campaign, but he struck in the 15th minute as Bordeaux won 1-0 at Troyes.
The win moved Gourvennec's side up to 13th place, while Troyes is 16th.
Lille climbed into 14th spot with a 1-0 win at Caen. Striker Nicolas Pepe scored his fifth of the season and both sides had a player sent off either side of halftime.
Also, striker Nolan Roux scored an 89th-minute equalizer as last-place Metz drew at mid-table Dijon 1-1.
Angers and Toulouse can both move out of the relegation zone on Sunday, providing they win away from home.
Angers, which is in 19th place, has a tall order given that it is at Lyon.
Meanwhile, 18th-place Toulouse is at 17th-place Saint-Etienne with only one point separating them.
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