Lille returned to the top of Ligue 1 despite a 0-0 draw at home to Brest on Sunday, while Wissam Ben Yedder scored an injury-time equaliser for Monaco as their seven-game winning run was ended by a resurgent Lorient.
Christophe Galtier's Lille failed to register a single shot on target as they dropped points for the first time in seven matches, moving back one clear of Paris Saint-Germain at the summit.
Canada international Jonathan David had a goal disallowed for Lille in the second half following a handball in the build-up by centre-back Jose Fonte.
"It's disappointing not to have won, but my disappointment is minimal when I see what we did going forward. It wasn't enough," said Galtier.
"We had an incredible opportunity with other results going our way and you need more character and personality in this type of match."
Ben Yedder netted twice for Monaco in a 2-2 draw as Lorient became the first team to take a point off Niko Kovac's side in the new year.
Nigerian striker Terem Moffi converted a penalty to give Lorient the lead on seven minutes at the Stade Louis II after Monaco goalkeeper Benjamin Lecomte brought down Yoane Wissa.
France striker Ben Yedder levelled from the spot early in the second half after a handball in the area, but Moffi put Lorient back in front on the hour with a composed finish after a loose pass from Djibril Sidibe.
The visitors looked on course for a fourth win in five outings only for Ben Yedder to hammer in a volley deep into stoppage time, for his 13th goal of the season.
"We earned a point. We didn't play as well as we have been. But that's part of the process. It's good to take a point in these conditions," said Kovac.
"It could be important at the end of the season. Never give up, never throw in the towel, that's what I want. This point reflects the team's DNA."
Monaco are fourth and six points back of leaders Lille, while PSG are second following Saturday's 2-1 victory over Nice. Lyon dropped to third after losing at home to Montpellier by the same scoreline.
Nantes snapped a run of 16 games without victory in all competitions, as Antoine Kombouare oversaw a 3-1 win at Angers in his first match since replacing Raymond Domenech.
Kombouare took over from Domenech in midweek after the former France coach was sacked following a brief spell lasting less than two months.
Saint-Etienne claimed a third win in four as they beat Rennes 2-0, while Strasbourg defeated Metz 2-1.
Nimes won 2-0 at Dijon as the two clubs swapped places at the foot of the table.
Marseille will attempt to secure a first league win in Bordeaux since 1977 in Sunday's late game.