It was a frustrating night for Nice, who were unable to break down Bordeaux and had Mario Balotelli and Younes Belhanda sent off in injury time.
Radamel Falcao scored again for Monaco as they beat Caen 2-1 to narrow the gap at the top to two points.
PSG hammered Lorient 5-0 and are now five points behind the leaders.
The reigning champions took the lead through Thomas Meunier's lob from inside the box before Zargo Toure deflected Edinson Cavani's cross into his own net to put Unai Emery's side firmly in control.
Thiago Silva headed home Lucas's corner to put the result beyond doubt while Cavani rubbed salt into Lorient's wounds by converting a penalty shortly after the hour for his 18th league goal of the season.
Lucas added a fifth with a lob 20 minutes from the end.
Falcao scored his 13th goal of the season as Monaco put last weekend's home defeat to Olympique Lyonnais behind them with victory at the Stade Louis II.
The Colombian opened the scoring from the spot after being brought down in the box before Tiemoue Bakayoko doubled the tally 14 minutes from full-time with a long-range strike.
Herve Bazile pulled one back in stoppage time for Caen, who had been reduced to 10 men when Damien Da Silva was dismissed in the 51st minute.
At the Nouveau Stade de Bordeaux, Nice allowed their frustration to get the better of them as Balotelli was shown red late on for kicking out at Igor Lewczuk after the Polish defender had grappled with him for the ball.
Moroccan international Belhanda was also dismissed minutes later after an opponent was left on the floor following a tussle for the ball.
Elsewhere, fourth-placed Lyon claimed their fourth win in a row as Alexandre Lacazette and Nabil Fekir scored in a 2-0 triumph over Angers and Bafetimbi Gomis netted his 10th goal of the campaign to help Marseille beat Bastia 2-1 and go level on points with fifth-placed Guingamp.
Nice will head into the winter break on top of Ligue 1 but their goalless draw at Bordeaux enabled both Monaco and Paris St-Germain to make up ground.