Neither side will look back on the opening half with any particular pride, although Bordeaux were at least able to muster some shots on goal.
Matthieu Chalme stung Petr Cech's palms with a drive from the right side of the box after 20 minutes, then seven minutes later Yoann Gourcuff - on loan from AC Milan - showed his class.
The 22-year-old picked up the ball 30 yards out with his back to goal, turned while pirouetting before striking a drive low to Cech's left where the Czech keeper made a good save.
The home fans must have been thankful for that touch of class because Chelsea provided nothing that can be described as such, only demonstrating again the limits to playing Nicolas Anelka up front on his own.
There were certainly no problems around Didier Drogba's fitness, leaving Blues fans to conclude that his starting on the bench was down to his recent musings over a potential move away from London.
The second half started as the first had ended, with hopeful balls forward to Anelka failing, while the home side's smarter passing looked more attractive but equally as unproductive.
Yet just as Chelsea boss Luiz Felipe Scolari was about to send on Drogba, presumably to save the day, last year's Champions League finalists found themselves somehow ahead.
With Bordeaux's Matthieu Valverde yet to make a save, Frank Lampard's quick, clever pass through the home defence found Anelka onside and the Frenchman side-stepped the keeper and found the open net.
It was an unlikely goal and yet it was enough to set Chelsea up for what looked for most of the rest of the half to be a sneaky away win.
The French side, sixth in their domestic league, had other ideas and did more than most in not giving up and sticking to their largely patient style of football.
So with seven minutes left, the hard-working Joe Cole gave away a corner that Gourcuff hit to the front post where Alou Diarra rose free to head in - leaving all eyes on his marker John Terry and on the joy of the home fans.
A needless sliding tackle on Fernando Menegazzo by Lampard earned the England international his second yellow card - enough to keep him out of the final, must-win, group game with CFR Cluj - and condemning his side to a frantic last five minutes.