Franck Azema's men went into the game full of confidence after scoring 18 tries in their first three matches, but struggled for fluency and had to fight back from a 13-11 half-time deficit.
But Beheregaray scored a 76th-minute try, and former Scotland captain Laidlaw kicked the extras and a penalty shortly after.
"It was not magic, but essential," said coach Azema. "I'm not saying it looked good, but it's a victory and the positive spiral goes on, and now we have to be honest on Monday in training and know what to work on."
Former New Zealand back Colin Slade starred in the first half for Pau, kicking five points and scoring a 34th-minute try to make it 13-6, but Clermont wing Remy Grosso touched down just before the break.
Spain international winger Charly Malie scored Pau's second try early in the second period, though, with Slade slotting over the conversion to increase their lead to nine points.
But scrum-half Laidlaw was introduced and kicked two penalties as Clermont went into the final five minutes trailing by six.
And Beheregaray crashed over with time running out, and the 32-year-old Laidlaw did the rest to continue Clermont's return to form after a miserable title defence last season which saw them finish ninth.
Elsewhere, reigning champions Castres jumped up to second in the table with a 29-13 win over newly-promoted Grenoble, who have lost four games on the trot.
Hooker Marc-Antoine Rallier scored two tries, while Argentinian fly-half Benjamin Urdapilleta kicked 12 points including a first-half drop goal.
Toulouse are level on points with Castres in third place, after a 30-17 home victory over Racing 92.
The capital-city side threatened a comeback despite slipping 21-3 behind, but two late penalties from Thomas Ramos ended their challenge.
"We had fun but we were still not out of sight because we were lax in the 50th minute," Toulouse centre Maxime Mermoz, who scored the opening try, told Canal+ Sport.
Lyon crush Montpellier
Earlier in the day, Lyon took revenge for a heavy defeat in last season's playoffs as they crushed Montpellier 55-13 to make it back-to-back wins.
Lyon scored eight tries to one by the visitors to earn a bonus point and climb to fourth in the table.
The hosts dominated and were repeatedly able to accelerate their play as they avenged their 40-14 loss in May.
"We were able to mix up our style of play and produce a match that sets the tone for our new players," said Lyon manager Pierre Mignoni.
"We really wanted to see a match like that, to see players sparkling on the pitch. And we only made seven mistakes. We played at a very high standard."
Montpellier, who finished top of last season's league table before losing in the playoff final, remained mired in the lower half of the Top 14.
They welcomed back several players, notably France back-row Louis Picamoles and fly-half Aaron Cruden but produced a display short on imagination and relying on power.
"Today, Lyon were better than us, especially in the second half," said Montpellier coach Vern Cotter. "To ship 50 (points) here is a lot."
After wing Toby Arnold gave Lyon a 22nd-minute lead, Montpellier briefly levelled the scores when prop Nico Janse van Rensburg pounced on a defensive mistake. But wing Noa Nakaitaci restored the home lead before half-time and Lyon ran riot after the break.
"In the second half it was a joke," said Montpellier winger Benjamin Fall. "Lyon played very well... We went missing today. We will give everything next week against Toulouse."
Scrum-half Baptiste Couilloud, Hendrik Roodt, lock Etienne Oosthuizen and centre Thibaut Regard scored four tries in 19 minutes for Lyon before Charlie Ngatai grabbed the last two.