Barguil outpowered three other breakaways, including Landa, to claim a much appreciated victory for the French on Bastille Day, the first local win on their national holiday in 12 years.
Thomas Voeckler (Direct Energie) and Barguil attacked straight from the gun, the Frenchmen looking to represent their nation on Bastille Day.
"Mikel was not a long way back overall and he's gained some important time", Froome countered.
The champion of Italy was dressed for the first time in his career the yellow jersey.
Britain's Chris Froome has lost the coveted yellow jersey in the Tour de France but remains on course to win the gruelling road race if the bookmakers' predictions are correct. Froome would have cracked no matter what, but symbolically, the image of the domestique zooming away from his captain was concerning.
Chris Froome had-until today-ridden a dream Tour de France, taking the yellow jersey on Stage 5 and enjoying the luxury of the peloton's strongest team insulating him from most every attack.
On Thursday Froome's Spanish team-mate Mikel Landa had been criticised by Sky sports director Nico Portal, after he failed to wait for the Briton when Froome struggled on the final climb.
Fabio Aru (Astana Pro Team) had big shoes to fill as he took over the leadership role of Astana from compatriot and 2014 victor Vincenzo Nibali. The Danish rider bravely took the stage start with fractures in his left wrist and elbow sustained in a crash earlier in the week.
Quintana and Barguil made contact with the leading pair and formed a working group, with only Barguil sitting out turns as he had little incentive to work. This jersey is an undescribable emotion, the maximum for a rider.
As Cummings started on the penultimate climb of the day, Col du Peyresourde, he had a 2 minute and 10 seconds lead on the group of favorites that were chasing behind. Bardet, perhaps the best descender, was the first, though his effort was fruitless. Aru now leads by six seconds from Froome with Bardet 25 seconds off the lead going into Friday's potentially explosive 101 kilometre dash from Saint-Girons to Foix. He tried to launch off his teammate, Kwiatowski, with roughly five kilometers to go, and Aru quickly on his wheel.
Froome was gracious in defeat, congratulating both Bardet and Aru, but he showed the steely determination that has helped him to win three Tours already. I stayed calm and focused.
The yellow jersey group would end 1:48 down on the stage victor, with Aru retaining the yellow jersey.
But the lead group kept clear, still almost two minutes ahead to pull Landa up to fifth, now just a minute down overall. Rivals might feel more deputized to take shots at Froome over the back nine of this Tour, especially with a time trial looming on the penultimate day. Unlike year's past, the 2017 Tour is gearing up for an exciting finish before Paris.
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