Bruno Genesio's Lille extended their unbeaten run in all competitions to 21 games with a 2-1 home win against Nice to move one point above Monaco, who had played earlier.
Despite taking the lead through Germany defender Thilo Kehrer in the first half against the league's worst defence, Monaco collapsed after the break when Jordan forward Mousa Al Tamari scored twice.
New signing Mika Biereth started in attack for coach Adi Hütter's Monaco, who have won only twice in the past 11 games overall.
It was only Montpellier's third win in 18 league games.
Defeat left Monaco 12 points behind leaders Paris Saint-Germain and increased the pressure on Hütter.
Next up for Lille is a tough trip to Premier League leaders Liverpool in the Champions League on Tuesday, but Genesio's side is proving very resilient this season.
Lille fell behind in the 29th when midfielder Sofiane Diop turned the ball in after goalkeeper Lucas Chevalier spilled a right-wing cross from Jonathan Clauss.
Clauss was fooled by striker Jonathan David's dummy shortly after the break, however, and David astutely set up Hakon Haraldsson's equaliser. Then Clauss botched a clearance in the 63rd and defender Bafodé Diakité finished.
Nice dropped to fifth place and one point behind Monaco.
Meanwhile, PSG, who take on Lens on Saturday, have just announced the signing of Napoli striker Khvicha Kvaratskhelia until 2029.
Neither side disclosed the financial details of the deal, but media reports said the French champions a 70 million euros ($A116m) plus add-ons for the 23-year-old.
Kvaratskhelia arrives in the French capital after failing to reach an agreement with Napoli to extend his contract, which was due to run until 2027, with the winger requesting his exit last week.
The Georgia international had previously been linked with a move to PSG in the close season before he stayed for another season under new coach Antonio Conte.
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