Three-time Tour winner Froome faded badly on the brutal final climb of the 214.5 kilometre stage from Pau while Aru finished third to take the final bonus seconds on offer.
The Italian national champion now leads the Tour by six seconds from Froome, with Frenchman Bardet closing to within 25 seconds of yellow in third place overall.
Dan Martin impressed again yesterday, climbing into the top five on GC after an impressive ride on a gruelling day.
Astana’s Aru will wear the yellow jersey for the first time in his career, while Froome has handed it over for the second time in his, having also lost it after stage four in 2015 before reclaiming it three days later and carrying it to Paris.
But that came in very different circumstances, and Froome cut a dejected figure outside the Team Sky bus last night.
“It was a tough day for me in the final metres and my team-mates had done such an amazing job,” Froome said.
“But I didn’t have the legs to finish it off, it’s as simple as that. No excuses. I just didn’t have the legs on the final kick.”
How Froome might have wished for the legs he had on these same roads in 2012, when he was made to wait for Bradley Wiggins when he wanted to attack in search of a stage win.
But there was a key difference this year, with the stage finishing at the top of the airstrip used in the opening sequence of James Bond film Tomorrow Never Dies, and it was there Froome fell short.
“The finish is brutal,” Froome added. “Ramps of over 20 per cent, that’s a really hard finish and I can only say congratulations to Romain Bardet for winning the stage and to Fabio Aru for taking the yellow jersey.”
Froome came into this race expecting Richie Porte to be the biggest threat to a third straight Tour crown, but though the Australian has crashed out, he has found himself in his toughest battle yet.
AG2R La Mondiale’s Bardet timed his attack to perfection, taking victory ahead of Aru and Colombian Rigoberto Uran of Cannondale-Drapac, both two seconds back but each picking up bonus seconds.
Uran sits fourth in the general classification, 55 seconds back after being docked 20 seconds for taking an illegal bottle in the final five kilometres. Video suggested Bardet may have done the same with 6.4 kilometres left but there was no penalty for the Frenchman.
It was a third career stage win for the 26-year-old, who finished second overall last year.
“I’m feeling very, very happy for sure,” he said. “This was maybe the hardest (win) to get but I will try to enjoy it. Tomorrow is another very hard stage and though I’m here for stage wins I’m here for the overall too, so we have to stay focused.”
Froome was left trailing in Bardet’s wake, coming over the line in seventh place some 22 seconds behind, beaten to the line by his team-mate Mikel Landa, Martin (Quick-Step Floors) and UAE Team Emirates’ Louis Meintjes.
Orica-Scott’s Simon Yates finished ninth in the young riders’ white jersey, but the Lancastrian surrendered 20 seconds to his rival Meintjes.
Yates leads the young riders’ classification by two minutes and 38 seconds from the South African.
Aru did not even plan on racing the Tour at the beginning of the season, but switched his attention to France after a knee injury ruled him out of the Giro d’Italia in May.
“It’s the biggest thing that could happen to me,” the 27-year-old said of taking yellow. “I never imagined it could happen. The stage was very, very hard and I’m very pleased to wear this jersey for my team-mates.”
Keeping it will not be easy. Today’s 101km stage from Saint-Girons to Foix is expected to be a full-on battle, and Aru will have to face it with a weakened team.