Lyon slumped to 17th in the standings with five points from six games, just above the relegation zone and trailing leaders and arch-rivals St Etienne, whom they host next weekend, by eight points.
Lyon, champions seven years in a row from 2002, lost striker Lisandro Lopez with an achilles injury before succumbing to second-half goals by Alou Diarra and Jussie.
Playmaker Yoann Gourcuff, who joined Lyon from Bordeaux during the close season, was booed throughout the match and produced yet another below-par performance.
"Fair play is not the Bordeaux crowd's prime quality," Lyon president Jean-Michel Aulas told French TV channel Canal Plus.
"It's a big disappointment because it was already a turning point. We had a good first half but unfortunately we could not do better," keeper Hugo Lloris added.
"It's a shame but we will continue to work hard."
Claude Puel's side were hoping to get into their stride following a 1-0 home win in their Champions League opener against Schalke 04 on Tuesday, but Bordeaux, who have also made a poor start this season, had other ideas.
In a packed Chaban Delmas stadium, the visitors had the first clear chance but Argentine Lisandro failed to find the target after being nicely set up by Jimmy Briand.
HEADED HOME
Bordeaux piled on the pressure after the break and they were rewarded on the hour when Diarra headed home from a Jaroslav Plasil free-kick, forcing Puel to make changes.
Striker Bafetimbi Gomis replaced winger Michel Bastos but the French international inexplicably missed the target from close range on 72 minutes.
Gomis then hit the bar after Bordeaux keeper Cedric Carrasso deflected his fierce shot from inside the box one minute from time.
Brazilian midfielder Jussie picked the ball up just into the Lyon half, slalomed through the defence, paused and coolly slotted home two minutes into stoppage time to wrap a deserved victory.
Earlier, Stade Rennes kept their unbeaten record but squandered the chance to go top of the table with a goalless draw at Paris Saint-Germain.
The Brittany side, third in the standings with 12 points, one adrift of leaders St Etienne, dominated at the Parc des Princes but were wasteful in front of goal.
Rennes striker Victor Hugo Montano had a clear chance on the stroke of half-time but his fierce shot shaved the bar.
PSG, who beat Sevilla 1-0 away in the Europa League on Thursday, looked jaded and happy to settle for a dull draw.
A last-gasp Moussa Sow goal gave Lille a 1-0 home win over AJ Auxerre as the unbeaten northerners climbed to sixth.
