While surprise packages Lille were again celebrating, Jean Tigana was plunged into despair and resigned as Girondins Bordeaux coach after yet another defeat where fans barracked his daughter.
Belgian winger Hazard, one of the most talked about young prospects in Europe, surprised the goalkeeper with the 20-metre free-kick and left third-from-bottom Nancy a point from safety.
There were very few chances in Nancy but Lille did just enough for victory even if they had a very late scare when Morocco's Youssouf Hadji went close.
Lille had suffered a mini-wobble as they seek their first title since 1954 but last weekend's 5-0 hammering of Arles-Avignon has re-establised their confidence.
Paris Saint-Germain earlier drew 1-1 at strugglers Monaco to move above Lyon into the third Champions League qualifying slot, nine points from the top.
Tigana quit after Bordeaux's hopes of a Europa League spot were hit by a 4-0 home thrashing by Sochaux, who occupy what is set to be the final Europa berth in sixth.
His daughter being verbally abused in the stands was the final straw.
"People think the problem is Jean Tigana," he said. "They go up and be aggressive to a girl of 16. I find that dramatic. For me that is not football. Good night. That was the last press conference I will give you."
FC Lorient in seventh did their European ambitions no favours with a 0-0 draw with Toulouse.
St Etienne are also one adrift of Sochaux after Alejandro Alonso's 32nd minute penalty secured a 1-0 victory at relegated Arles-Avignon.
In the lower half, Auxerre pushed themselves further away from trouble with a 1-0 home success over Montpellier but second-from-bottom Racing Lens are eight points from safety and almost doomed following a 1-1 draw at fellow strugglers Caen.
