The French champions, who have already qualified for the knockout stage, have 13 points, five ahead of second-placed Juve with a game to spare.
Juventus, who suffered their first defeat in the group stage this season, will join Bordeaux in the knockout phase if they do not lose at home to Bayern Munich in their next game.
"Our fate is still in our hands. We didn't play a good game tonight but that doesn't ruin our chances to qualify," Juventus coach Ciro Ferrara told reporters.
"Juventus are strong enough to beat Bayern at home and to go through. It won't be easy but we can do it," he added.
Bordeaux snatched a fourth consecutive win in the Champions League through goals by midfielders Fernando and striker Marouane Chamakh.
"I am very happy and very proud of my team. We were well prepared and each player sacrificed himself for his team mates," Bordeaux coach Laurent Blanc told reporters.
"It was a tough draw but we have been able to rival those teams (Bayern and Juventus) as the results show."
The French champions got off to a better start despite playmaker Yoann Gourcuff's absence through injury and their passing game helped them dominate throughout the first half.
Their best chance came just before the interval when defender Matthieu Chalme set up Marouane Chamakh in the box but the Morocco striker's effort from close range was saved by Gianluigi Buffon.
Bordeaux eventually broke the deadlock nine minutes into the second half when midfielder Fernando headed in a Jaroslav Plasil free kick.
Fit-again Alessandro Del Piero made the starting line-up as a right winger but the Italian veteran failed to make an impact until he moved into a more central position in second half.
Del Piero created Juve's best chance before being substituted but Diego and Amauri both missed the ball at close range from one of his crosses.
Juventus tried to push harder to snatch a late equaliser but Chamakh sealed Bordeaux's win with a stoppage time header from a Wendel corner kick.
