The division's early pacesetter had scored 149 points across its opening three fixtures, but this was a more hard-fought success as Laidlaw sent over a conversion and a penalty in the final four minutes to seal a narrow win.
Clermont had scored 18 tries in its previous three wins but managed to add just two more through Remy Grosso and Yohan Beheregaray against a Pau side for which Colin Slade scored 12 points.
Reigning champion Castres is up to second in the standings thanks to a 29-13 win over Grenoble, which has lost each of its opening four fixtures since being promoted.
Hooker Marc-Antoine Rallier twice crossed the whitewash, as did Alex Tulou, while Benjamin Urdapilleta kicked nine points.
Lyon produced the most comprehensive victory of the day as it ran in eight tries in a 55-13 thrashing of Montpellier.
Jake McIntyre kicked five penalties in Agen's 22-17 success over Bordeaux-Begles, while Toulouse sealed a 30-17 win over Racing 92.