Monaco forward Anthony Martial, one of the most promising prospects in the league at 18, took a pass from James Rodriguez in the 16th and dribbled past three defenders to fire a low strike that Ajaccio goalkeeper Guillermo Ochoa palmed away.
Ochoa frustrated Monaco by tipping a powerful drive from Jeremy Toulalan over the bar in the 20th and saving a header from Ricardo Carvalho in the 56th from a corner.
Ajaccio was reduced to 10 men in the 62nd when Jean-Baptiste Pierazzi picked up a second yellow card for tripping Rodriguez.
Monaco capitalized on its numerical superiority to take the lead before striking the post twice with free kicks from Rodriguez in the 80th and playmaker Joao Moutinho in the 84th.
In Bordeaux, Landry N'Guemo fired a long-range strike in the 27th minute that deflected off Lille defender Simon Kjaer to beat goalkeeper Vincent Enyeama, who had not conceded a goal in his previous 11 league games.
Bordeaux went down to 10 men in the 58th when defender Maxime Poundje was sent off for clattering into Lille fullback Franck Beria.
A resilient Bordeaux side managed to protect its slim lead thanks to N'Guemo clearing a bicycle kick from Lille leftback Pape Souare off the line in the 84th.
"We've missed that solidarity to make the difference in some games," Bordeaux goalkeeper Cedric Carrasso said. "There's a state of mind which is emerging. We must try to keep it."
Lille lost ground in the title race and dropped to third place, four points behind PSG, while Bordeaux went level on points with fifth-place Marseille.
"We were not at the races this afternoon," Lille midfielder Rio Mavuba said. "We were beaten in our heads. They showed more desire than us."
In Bastia, Florian Raspentino converted a cross from Julian Palmieri to put the hosts ahead in the 34th. But Alexandre Lacazette equalized in the 54th before Yassine Benzia gave Lyon the lead by heading home a cross from Clement Grenier in the 56th.
Bafetimbi Gomis sealed the win in the 85th with an assist from fullback Henri Bedimo.
Bastia dropped to 12th after its first home loss this season.
In Toulouse, Abel Aguilar scored the equalizer in the 71st after Montpellier striker Souleymane Camara opened the scoring in the 19th.
Montpellier goalkeeper Geoffrey Jourdren stopped a penalty from Toulouse forward Eden Ben Basat following a foul from Daniel Congre, who was red-carded in the 49th.
Toulouse also lost a man in the 67th when Jonathan Zebina picked up a second yellow card for dissent.
On Saturday, it was: Paris Saint-Germain 5, Sochaux 0; Reims 1, Nice 0; Lorient 2, Rennes 0; and Valenciennes 1, Guingamp 1.
The match between Saint-Etienne and Evian was postponed because of a frozen pitch.
Marseille coach Elie Baup was dismissed Saturday after the 2010 champion lost 1-0 to Nantes the day before. Baup was replaced by sporting director Jose Anigo who will be in charge until the winter break.