Cilic was playing so cleanly until that moment, delivering 12 winners before his initial unforced error; he would finish with a 70-21 margin.
Froome's teammates had set a fast tempo that prevented others from attacking-a tactic that prepared the ground for Froome's expected assault in the steep final section leading to the finish in the ski station of Peyragudes. His attack was followed by Alberto Contador (Trek-Segafredo) who was also joined by Mikel Landa (Team Sky).
On the descent, attacks flowed from all of the favourites as it became a game of cat-and-mouse between the big names of the Tour.
Not only did Aru strip Froome of the yellow jersey but the top of the standings closed up with Frenchman Bardet now third at just 25sec.
Patrick Rodgers shot a seven-under-par 64 to take a two-shot lead after the second round of the John Deere Classic in Silvis, Ill.
Barguil is the first French rider to win a Tour stage on Bastille Day - France's national day - since David Moncoutie in 2005.
He said he had visited the ski station with his parents to scout out the final climb.
"Landa is here now, but today I could not follow everyone". First was, a lead group of four riders - Barguil and Quintana chased down Landa and Contador before the summit, and Barguil went over the top first to further cement the polka dot jersey.
The two are locked into a ding-dong battle, and though BMC's Roche expects Team Sky star Froome to maintain a strong push for glory, Aru's emergence has impressed the Irishman.
"It's one of the most beautiful things that can happen to you in life, wearing the yellow jersey", said Aru. "There's a few mountain stages to come", added Roche, 38th in the GC. "We're ready for that".
Quintana complained of fatigue having raced in May's Giro d'Italia, while Contador crashed four times over the first 11 stages. I think Froome is going to be able to keep his shape; it just looks like every time Aru goes, he goes. Landa was the biggest winner of the day, jumping from seventh to fifth, now 1:09 back. "He'll definitely try some more", Astana manager Alexandre Vinokourov said.
The Sky leader finished eighth on a short but tough Pyrenean stage, and said afterwards he felt in much better shape than Thursday. "Let's hope our guys find more motivation".
Kittel has lost only one sprint since the start and has been in a class of his own since Mark Cavendish and Arnaud Demare departed the race.
Bennett attacked with 500m left and tried to grab the stage victory.
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