Bordeaux scored just once in an entertaining game, with a diving header by Brazilian midfielder Wendel from a Benoit Tremoulinas cross on 23 minutes, but thrilled their fans with a string of clever moves.
The club from the wine capital moved top with 19 points from seven games, two points clear of second-placed Olympique Lyon, who had briefly taken command with a 2-1 home win over Toulouse on Saturday.
"We knew that Rennes were a strong side and it was tough but we wanted that first place badly," Bordeaux midfielder Mathieu Chalme told French television channel Canal Plus.
"This is a good way to prepare for Wednesday," he added, referring to Bordeaux's game at home to Maccabi Haifa in the Champions League.
Bordeaux, who ended Lyon's seven-year reign to take their first title in 10 years last May, have now gone 21 matches without defeat in all competitions.
Lille needed a last-gasp goal by striker Pierre-Alain Frau to salvage a 1-1 home draw with fellow strugglers Nice earlier on Sunday.
Frau fired in from 18 metres with one minute left to save Lille, lying 17th with just one win from seven games, from an embarrassing defeat.
Forward Loic Remy exploited a defensive blunder to put the visitors ahead on the hour but Nice had to be content with a share of the points and stay second from bottom in the 20-team standings.
Midfielder Frederic Thomas struck twice to help Le Mans to a comfortable 3-0 home win over Racing Lens which lifted them up to 15th.
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