Vincenzo Iaquinta had given the hosts the lead on 63 minutes when he fired past substitute goalkeeper Ulrich Rame after Fabio Cannavaro's ball forward outfoxed Bordeaux's defence.
Midfielder Plasil then poked in at the far post on 75 minutes after a shaky Juve defence had allowed a free kick to be flicked on.
The home side, in Ciro Ferrara's first European game as coach, were largely flat for much of the contest despite having won their first three Serie A games.
The French champions had just as many chances with Fernando slicing through Juve's backline early on and forcing Gianluigi Buffon into a smart save before again being denied by the Italy goalkeeper in the second period.
"I'm sorry. We strongly wanted to start with a win but we came up against a well-organised side. The Champions League is always difficult but there is time to put it right," Ferrara told a news conference.
"Buffon has been phenomenal on a couple of occasions. I am a bit worried but it is normal. I don't want to find excuses."
"We worried Juventus and could have won," Blanc said." I'm happy with the result as before the match I would have taken a draw. What gives me more pleasure is how we played."
