Clermont are five points ahead of Montpellier and Toulon and 10 in front of Bordeaux
Clermont have 32 points, five ahead of Montpellier and Toulon and 10 in front of Bordeaux, who occupy the sixth and final play-off spot.
Argentine fly-half Patricio Fernandez scored two tries for Clermont, book-ending further scores from promising young scrum-half Charly Cassang and Fiji winger Noa Nakaitaci.
Fernandez was also perfect with the boot, hitting four conversions and four penalties for a personal haul of 30 points -- a record for a player in one match this season.
"We are happy with the character and performance of the young players. They were under pressure early in the game but they did not let up," said Clermont coach Franck Azema, whose side were the last team to win at Brive.
"This derby is a battle of the Massif Central. It's important to win it because it has a special flavour, especially because besides it being a derby, we know that it's very complicated to come here."
Earlier, Castres held on to beat Bordeaux-Begles 33-27 in a six-try thriller.
But Bordeaux left without even a losing bonus point -- awarded when teams lose by five points or less -- after former France fly-half Lionel Beauxis missed with a last-minute penalty attempt.
The visitors had been on the rampage leading up to that attempt with New Zealander centre Jayden Spence missing out on a try when he spilled Beauxis's up-and-under in the Castres end zone.
In a thrilling start, Castres fly-half Benjamin Urdapilleta kicked two penalties before the hosts were awarded a penalty try on 11 minutes after a deliberate knock-on from Bordeaux's Fiji wing Metuisela Talebula prevented a certain try.
Despite Talebula also getting a yellow card Bordeaux struck back on 15 minutes when scrum-half Baptiste Serin sold a dummy to lumbering prop Daniel Kotze before scampering over.
"We made it difficult for ourselves after a great start, and Serin's stroke of genius contributed to that," said Castres lock Loic Jacquet.
Yet on 20 minutes Castres put together a fluid move that ended with Samoan wing David Smith passing inside for centre Thomas Combezou to score.
Urdapilleta and Ireland fly-half Ian Madigan exchanged penalties before Bordeaux closed out the half with a try from full-back Jean-Marcellin Buttin down the right following quick hands in the backs.
Madigan's conversion left Castres leading 23-17 at the end of an exhilarating first half.
The second half didn't live up to the first until replacement Castres scrum-half Antoine Dupont scored a carbon copy of Serin's earlier try, sending Talebula the wrong way with an outrageous dummy.
Bordeaux wouldn't lie down and Spence finished off another blistering attack to dot down in the corner.
On Saturday, three-time European champions Toulon gave new coach Mike Ford a winning Top 14 start with a commanding 42-12 victory over struggling Grenoble.
Toulon ran in six tries for the winning bonus point with Mathieu Bastareaud, Mamuka Gorgodze, Jocelino Suta and Axel Muller all crossing.
"It was a good match, a good start, we won with the bonus point, which is very valuable in this competition," said Ford as Toulon went provisionally top on the night.
Montpellier edged out La Rochelle 12-11 thanks to a dramatic last-minute penalty from Ben Botica.
Defending champions Racing 92 won their first away match of the season, defeating rock-bottom Bayonne 16-3 despite playing without star fly-half Dan Carter, who was injured in the warm-up.
Toulouse also earned their first away win of the season in a 24-20 success at Pau while 2015 champions Stade Francais beat Lyon 25-19.