Paris Saint-Germain top the table on 36 points, four ahead of Nice in second, six ahead of Monaco, who lost to Lyon on Friday, and nine ahead of Lille, who they play Sunday.
This new Nice defeat means PSG go into the winter break top of the league and, given Le Havre had failed to win in their last nine outings, is also a worry for challengers Nice.
The Riviera outfit had only conceded six goals in 15 games before Saturday but Le Havre's American striker Emmanuel Sabbi scored twice and Mohamed Bayo added a third before Raoul Louche notched a Nice consolation goal in time added on.
An 85th-minute winner from Jeffinho gave Lyon a 1-0 away victory against Monaco on Friday, moving the seven-times Ligue 1 champions out of the automatic relegation spots.
That was a second straight win for Lyon and their interim coach Pierre Sage, who has made hit it off with the Lyon dressing room since taking over from the sacked Fabio Grosso at the start of the month.
Later Saturday, Lens host Reims while Lille's meeting with PSG is the pick of the six games on Sunday.
