Bordeaux-Begles kicked off to an early lead in the neck-and-neck game with two successful penalties via Camille Lopez’s boot to put them 6-0 up.
Lopez took a third to go ahead again after David Skrela’s own efforts had pulled Clermont level, before a dropped goal from Ludovic Radosavljevic and another Skrela penalty saw the visitors ahead for the first time at the break.
Regan King scored the only try of the match in the second half, converted by the omnipresent Skrela before the fly-half scored yet another penalty.
The hosts stole a shock 24-22 lead late in the game courtesy of tries from flanker Louis Madaule and hooker Wayne Avei, but Brock James came to the rescue off the bench and booted his own brace of penalties to drag Clermont over the line.
The result puts pressure on table-leaders Toulon, who sit three points ahead of second-placed Clermont and play struggling Agen on Saturday.