Second-placed Monaco are now four points ahead of Brest in third after the Brittany-based side's 0-0 home draw against Nantes.
The top three qualify automatically for the Champions League proper, with the side finishing fourth - currently Lille - going into the qualifying rounds.
Monaco are in pole position for a direct spot in Europe's premier club competition, 20 years after losing in the final to Jose Mourinho's Porto.
Ben Yedder's second-half double took him to 15 league goals this season.
He also netted twice last weekend against Lyon, and the 33-year-old sharpshooter has now scored 97 league goals since joining Monaco five years ago.
Ben Yedder is looking back to his best and could be in contention for a place in France's squad for European Championship, which kicks-off in Germany next month.
National coach Didier Deschamps names his squad on May 16.
Japan forward Takumi Minamino set up both of Ben Yedder's goals, having put his side ahead in the 16th minute with a curler into the top right corner.
Moments after Austria midfielder Muhammed Cham equalised for Clermont, Breel Embolo grabbed his first of the season to make it 2-1 to Monaco in the 37th minute.
Brest's chances of taking three points took a blow when midfielder Pierre-Lees Melou and winger Romain Del Castillo - the club's two best players this season - went off injured in the first half.
Midfielder Yassine Kechta scored twice and Ghana international Andre Ayew added a late third as Le Havre beat Strasbourg 3-1 to boost their chances of staying up.
Le Havre, who drew 3-3 at Paris Saint-Germain last weekend, are in 15th place - one point behind Nantes but three clear of Metz in 16th spot for the promotion-relegation play-off spot.
Metz lost 3-2 at home to Rennes, with striker Arnaud Kalimuendo grabbing the winner in stoppage time.
Georgia midfielder Georges Mikautadze put Metz ahead early with a brilliant lob from the right edge of the penalty area, but was sent off for barging into Kalimuendo moments after he scored.
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