A second-half goal from Henri Saivet was enough to earn Bordeaux the points in Nice as Les Girondins continued their recent impressive Ligue 1 form.
Bordeaux have now lost just one of their last eight league matches and leapfrog their hosts to fifth in the table.
It also marked their first victory at the Stade du Ray since 2005 and consigned Nice to only their second defeat in 12 matches.
The visitors made a good start and went close to taking a 10th-minute lead when David Bellion's volley took a telling deflection off Renato Civelli, but David Ospina was thankful to see the ball loop over his crossbar.
At the other end, Timothee Kolodziejczak danced past Saivet and Mariano before testing Cedric Carrasso with a right-footed effort, but the goalkeeper got down well to turn his effort away.
With the game now in full flow, Bordeaux worked another good opening. Ludovic Obraniak provided Saivet with a shooting chance but he dragged his volley wide of the left post.
The end-to-end action continued and Nice's Eric Bautheac was unfortunate to see his acrobatic effort countered by Mariano after Dario Cvitanich had worked the opening well.
With neither side finding the breakthrough before half-time, it was Bordeaux who took the initiative in the second period just before the hour mark.
Pressed by Kevin Anin and Fabrice Abriel, Jaroslav Plasil did well to pick out Saivet, who caught Ospina off-guard with a powerful shot at the near post to open the scoring.
The hosts failed to respond and it was Bordeaux who went close once again with Obraniak seeing his deflected shot finish up in the side-netting.
Nice coach Claude Puel threw on Neal Maupay with 25 minutes remaining and the substitute almost made an immediate impact.
The 16-year-old showed good skill to control the ball before attempting to lob Carrasso but, with the keeper beaten, the ball rebounded back off the crossbar.
Nice continued to press and nearly got their reward in the dying seconds but for a magnificent save by Carrasso. Bautheac swung in a dangerous free-kick and Civelli thought he had scored the equaliser with his head, only to be denied impressively by the keeper.