Nicolas Roche enjoyed his best performance of the Tour de France so far as Dutchman Bauke Mollema of the Trek-Segafredo team won the 15th stage, a 189.5-km ride from Laissac-Severac L'Eglise on Sunday.
BMC's Roche finished sixth as part of a group chasing down Mollema, who jumped away from the breakaway 31km from the finish to claim a solo victory ahead of Italian Diego Ulissi and Frenchman Tony Gallopin.
Quick-Step rider Dan Martin finished 25th and moves up to fifth in the General Classification, 72 seconds off yellow jersey holder Chris Froome.
Froome had needed a wheel change when the race was on approaching the Col de Peyra Taillade, and lost almost a minute before spending eight kilometres chasing his way back to the group of main contenders.
But the three-time Tour winner held on and retains his lead of 18 seconds over Italian Fabio Aru, with Frenchman Romain Bardet a further five seconds down in third place.
Bardet's AG2R La Mondiale team had upped the pace as the category one Peyra Taillaide - the penultimate climb of the day - approached with around 40km left, and had already distanced Froome once before the Team Sky man was forced to pull over.
Froome took a quick wheel change from Michal Kwiatkowski before Mikel Nieve and Sergio Henao helped pace him up the climb.
Mikel Landa then answered questions about his loyalty to the cause by dropping out of the lead group to finish the job, and Froome clung on as Bardet tried a brief attack before the summit.
The main group of contenders marked each other over the rolling final kilometres, but Martin was allowed to pull clear with around eight kilometres left and claw back more time.
The Irishman, still feeling the effects of a stage nine crash, picked up 14 seconds to move up to fifth place ahead of Landa, now 72 seconds off yellow.
It had been clear since midway through the day that stage honours would go to the breakaway, with Sky happy to let a 28-man group pull further and further away.
German Tony Martin tried his luck with a long-range attack, but after the Katusha-Alpecin man was caught on the Peyra Taillade, there were a series of attacks and counter-attacks.
Mollema attacked on the descent of the Peyra Taillade, and held off a chasing group of Warren Barguil, Primoz Roglic, Diego Ulissi, and Tony Gallopin over the final categorised climb, the Cote de Saint-Vidal, to ride to the finish alone.
"It's really amazing," Mollema said. "I'm so happy to win a stage at the Tour de France. I've worked for it so hard in the last few years. That was a big goal for me.
"I just gave it a try in the last 30km. It was a long time riding alone. It was close to the chases at the end. But I made it. This is the biggest win of my career so far. The Tour de France has always been my dream. I'm incredibly happy."