Jefferson Poirot's early try put Bordeaux ahead, but normal service seemed to have been resumed at the end of the first half when Castres went ahead with a penalty try.
Early in the second half Castres pulled clear as Yannick Caballero scored a try while the hosts had a two-man advantage, following yellow cards three minutes apart for Tamato Leupolu and François Tisseau.
Julien Seron had other ideas, scoring a try for Bordeaux with 18 minutes left to get them back into the lead.
Rory Kockott landed his third penalty of the match six minute later to put Castres three points clear, but Bordeaux kicked Federico Nicolás Sanchez ensured the match ended in a draw as he landed his third penalty with the clock three minutes into the red.
The result sees Castres left fourth on 68 points, five adrift of third-placed Toulouse and five ahead of fifth-placed Racing Metro.
Bordeaux are 12th, but safe from relegation as they are 16 points clear of Agen below them.
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