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 visitor 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.
Meanwhile, crisis-hit Marseille held out for over half an hour with only nine men to secure a goalless draw against toothless Bordeaux.
OM, without a league win since January 6, had claimed a morale-boosting French Cup victory in midweek against Auxerre, their first success under stand-in coach Nasser Larguet.
Any hopes of another win were ended in the space of five second-half minutes.
Argentinian defender Leonardo Balerdi was dismissed in the 55th minute for cynically pulling back Remi Oudin, before striker Dario Benedetto received his marching orders for a horrendous tackle on Laurent Koscielny.
But Bordeaux, on a run of four straight losses in all competitions, were poor throughout and never seriously threatened a winner, with a succession of tame long-range efforts from Hatem Ben Arfa the best they could muster.
"We showed solidarity, Bordeaux did not have a lot of chances," said Marseille captain and goalkeeper Steve Mandanda.
"We'll take the little positive because unfortunately at the moment we have a lot of things against us."
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 it 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.