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.
