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.
Monaco climbed to second on 21 points with a 3-1 win at 10-man Boulogne thanks to two late goals by Ligue 1 top scorer Nene, who took his tally to nine goals this season.
Surprise packages Montpellier squandered the opportunity to go top when they lost 3-0 at Stade Rennes. The promoted side stay on 20 points, behind Lyon on goal difference.
Bottom club Grenoble suffered their 10th defeat in as many games when they lost 2-1 at home to Nancy.
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
Morocco striker Marouane Chamakh, who had not found the back of the net since mid-August, and substitute David Bellion completed the scoring in the second half.
Lyon were sunk by three of their former apprentices at Nice, four days after their convincing 2-1 win at Liverpool in the Champions League.
"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.
The first was headed in by striker Mamadou Bagayoko and the second was deflected into his own goal by Aly Cissokho as Lyon goalkeeper Remy Vercoutre was unable to stop the ball from trickling across the line.
Nice, 14th on 11 points, made the best of their counter-attacks in the second half.
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.
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