Bordeaux have 22 points from 10 games, two ahead of Lyon who slumped to third following their second consecutive league defeat.
"Our own result is the most important thing but when we heard that other results were also in our favour, we were even more delighted," Bordeaux coach Laurent Blanc told reporters.
In heavy rain, Bordeaux dominated their match against Le Mans and took an early lead through an own goal by visitors' goalkeeper Didier Ovono.
Bordeaux forward Yoan Gouffran collected the ball in the box after a cross by Jaroslav Plasil. His shot hit the post and bounced off Ovono's shoulder before crossing the line.
LYON NIGHTMARE
"This game was an ordeal. I loved our game in Liverpool as much as I hated this one. I feel bad," Lyon coach Claude Puel told reporters.
"We lacked drive. Maybe I should have made more changes from the side that played on Tuesday."
Loic Remy set up Nice's first two goals with two crosses before the interval.
David Hellebuyck netted the third from a defence-splitting pass by Anthony Mounier before Remy put Nice's win beyond doubt despite a late goal by Ederson. Hellebuyck, Mounier and Remy are all former members of Lyon's youth academy.
The game was played despite a suspected swine flu case in Nice's squad, the French League said.
