Alou Diarra headed in a late equaliser to give Bordeaux a deserved point which leaves Chelsea sweating over their participation in the knockout phase of the Champions League heading into their final group game against CFR Cluj.
Chelsea struggled to create anything all night, but went ahead when Frank Lampard released Nicolas Anelka to dispatch the ball past Valverde.
However, Bordeaux hit back when Diarra was left unmarked at a corner to head in past a helpless Cech.
Lampardâ€™s dismissal for a second bookable offence compounded a miserable night for the West London side.
In truth, the Blues never really got going. The first half was dominated by Bordeaux, who had a number of efforts on target. Cech was forced into action throughout, having to repel efforts from Fernando, Chalme and Gourcouff.
Chelsea on the other hand created virtually nothing. Possession was surrendered easily and Nicolas Anelka was proving to be ineffectual upfront, and was flagged for being offside on a number of occasions.
The second half continued in the same vein, but then Chelsea landed a sucker punch and took the lead.
Anelka sprang into life and ran onto Lampardâ€™s expert pass, feinting twice before dinking it over Valverde to give Chelsea a barely deserved lead.
Didier Drogba replaced the Frenchman moments later, and it then appeared as if Scolariâ€™s men would hold on and seal the three points, but some sloppy marking from a corner put paid to that idea. Diarra was left totally free from a corner, and had the simple task of steering the ball in, via the post.
Chelsea never looked like conjuring up a response, and their night went from bad to worse when Lampard received his marching orders for a tackle on Fernando.
While Chelseaâ€™s away form in the Premier League is exemplary, their exploits on the road in Europe have left a lot to be desired.
Another European nightmare means that the Matchday 6 encounter with CFR Cluj is now a must win game if Chelsea want to have any chance of appearing in Rome in May.