League leaders Clermont had looked certain to end that record as they took a 13-6 lead ten minutes into the second half with a breakaway try from Jean Marcelin Buttin, who ran the length of the pitch after Jan Bornman split the ball as his side pushed for a try.
Castres fly-half Rory Kockott had missed five penalties during the match, but made up for it with a try 17 minutes from the end thanks to a break by flanker Antoine Claassen.
Replacement full-back Romain Tuelet had by then taken over kicking duties, and landed the conversion to level the scores at 13-13 before adding a penalty five minutes from time to secure the victory.
