Defending champion PSG was missing Kylian Mbappe through suspension and was without the injured Neymar, while striker Moise Kean was ruled out after testing positive for the coronavirus earlier Wednesday.
Winger Pablo Sarabia filled in and scored in the 20th minute when he turned in Idrissa Gueye’s cross from the left.
Bordeaux winger Hatem Ben Arfa should have equalized against his former club when he ran through in the 70th, only to shoot just wide of the left post.
The top three sides all won 1-0, with Lyon edging out Rennes at home to stay one point behind of PSG.
Lyon is now four points clear of fourth-place Monaco after it lost 1-0 at Strasbourg for a first defeat in 13 league games.
Lyon forward Memphis Depay created the winning goal for substitute Houssem Aouar in the 73rd minute.
Depay sprinted through down the right, but then lost his balance after shrugging off a defender just outside the penalty area. He got quickly back up and slid-tackled the ball to Aouar, who clipped the ball neatly over the goalie.