Colombian striker Falcao was again ruled out by a muscle injury that sidelined him for cup wins over Yzeure and Nice, and Monaco couldn't break down the league's meanest defence without their top scorer.
Brazilian left-back Jorge drew an excellent stop from Montpellier goalkeeper Benjamin Lecomte, who then pulled off a terrific reflex save to deny Kevin N'Doram to preserve a 10th clean sheet of the season.
The stalemate at the Stade de la Mosson snapped Monaco's four-match winning run in Ligue 1 but sent them a point clear of Lyon in second, while leaving them eight points adrift of leaders Paris Saint-Germain.
Christophe Galtier made a winning start in his first league game in charge of Lille after replacing the sacked Marcelo Bielsa just before Christmas.
Nicolas Pepe's 43rd-minute goal handed Lille a 1-0 victory at Caen and also prompted the dismissal of home goalkeeper Remy Vercoutre after he took umbrage at the Ivorian winger's exuberant celebration.
The veteran Vercoutre was incensed by Pepe's 'robot' dance in front of the home fans and argued furiously with the goalscorer over what he felt was a provocation.
Pepe appeared to be playing it up for a pitchside camera, and the 37-year-old Vercoutre was shown a straight red card. However, Lille also finished the match with 10 men after Fode Ballo-Toure was sent off early into the second half.
Thauvin on target
Florian Thauvin scored his team-leading ninth goal of the season but also missed a penalty as Marseille brushed aside Rennes 3-0 at Roazhon Park.
The former Newcastle winger saw a first-half spot-kick saved by Rennes goalkeeper Tomas Koubek but redeemed himself by setting up Valere Germain for the opening goal on 35 minutes.
Thauvin's ninth assist of the season drew him level with Neymar, while Hiroki Sakai produced a brilliant goal-line block to deny Ismaila Sarr an equaliser, and minutes later Germain teed up Morgan Sanson to rifle in Marseille's second just before half-time.
Thauvin completed the scoring eight minutes from the end when he nodded in a cross from Brazilian midfielder Luiz Gustavo.
Marseille avenged a 3-1 defeat by Rennes at the Velodrome in September -- one of just three losses for Rudi Garcia's team this season -- to move level on 41 points with third-place Lyon.
Nice continued their resurgent form as Pierre Lees-Melou's deflected strike earned them a 1-0 home win over Amiens, while a Gaetan Laborde header gave Bordeaux a 1-0 victory at Troyes to halt a run of six straight defeats in all competitions.
Edinson Cavani is in line to return for PSG at Claudio Ranieri's Nantes on Sunday after missing their last two matches following his delayed return from holiday, but Neymar has been sidelined by a rib injury.
Lyon will go in search of a fifth straight league win when they host second-from-bottom Angers, but they will be without joint-top scorer Mariano Diaz as he recovers from a hernia operation.