The Basque outfit, who shocked Racing 92 in Paris last weekend, led 24-19 at the break as Maxime Lamothe and Peyo Muscarditz scored early tries before former New Zealand centre George Moala responded for the visitors.
Apisai Naqalevu and Charlie Cassang then dotted down in the second half to move Clermont to the top of the table with their second win of the new campaign.
Later on Saturday, the pick of the ties sees Toulon head to Bordeaux-Begles after both sides picked up impressive wins in the opening round of action.
Agen host the other new faces in the top flight, Brive, Pau travel to Montpellier and La Rochelle welcome Stade Francais.
On Sunday, Racing 92 play Castres and champions Toulouse, without 13 players on Rugby World Cup duty, face a trip to Lyon.