The two sides, separated by 21 points last term, with Bordeaux missing out on the play-offs, each have 13 points through three matches, having won at Castres and Toulon respectively on Sunday (AEST).
Bordeaux scored the only two tries of the first half against Castres through Scott Higginbotham and Matthieu Jalibert, but still trailed at the end of an entertaining first 40 minutes.
Rory Kockott kicked five penalties before the break, although he ended the half in the sin bin. Masalosalo Tutaia had earlier seen yellow for the visitors.
Bordeaux led for much of the second period, moving in front through Tutaia's 48th-minute effort, but it appeared Castres would still triumph, with Benjamin Lapeyre and Thomas Combezou going over.
Ultimately, it came down to a penalty try four minutes from time for Bordeaux to run out a 34-32 victor.
Lyon was far more comfortable in a 20-6 success at Toulon, despite seeing both Patrick Sobela and Jeremie Maurouard sent to the bin late on.
It was 3-3 at the break but tries from Clement Ric and Pierre-Louis Barassi saw the away side cruise.
Elsewhere, Paul Willemse scored a pair of tries as Montpellier defeated La Rochelle 30-16 at home with a strong second-half showing.
Stade Francais edged past Bayonne 33-27, while Pau left it late to beat Agen 18-12.