For his third place, Froome was awarded four bonus seconds that allowed him to consolidate his overall lead.
Richie Porte and Geraint Thomas, two of the top five contenders at the time, quit the Tour de France in pieces after crashing on wet and slippery descents.
He caught lone escapee Warren Barguil of Team Sunweb inside the final 15km and left him behind, but Froome, Uran, Aru and Jakob Fuglsang of Astana worked well together and mopped up first Barguil, before catching Bardet.
“I had a mechanical problem with my gears, I had to change bikes”, said three-time champion Froome.
Dan Martin [Quick-Step Floors], who was brought down by Richie Porte [BMC] when the latter had his terrifying high-speed accident, had alleged that Tour organisers had “got what they wanted” by placing the Mont du Chat, with its steep, narrow, twisting descent, at the end of a long stressful day in the saddle.
Froome, who leads Aru by 18 seconds after nine stages, said during Monday’s first rest day that he just made a mistake.
The good news for British cycling fans was that Chris Froome retained the yellow jersey with a ride of real guts but the bad news was his compatriot and Team Sky teammate Geraint Thomas crashed out of the tour.
Thomas, second overall before Sunday’s stage, also had to quit the tournament for collarbone fracture suffered in an earlier crash.
BMC manager Jim Ochowicz said the team had suffered a “brutal” blow, but vowed to fight on.
“Crashes, risky descents, attacks from all my rivals, mechanical incidents – it just didn’t stop”.
Marcel Kittel has already won three stages and will be favourite to claim two more in the next two days, his German compatriot Andre Greipel, and Norwegians Alexander Kristoff and Edvald Boasson Hagen perhaps the only two competitors who’ve shown any hope in previous sprints of beating him. He had been 25 seconds off Froome’s yellow jersey but now finds himself a further one minute 19 seconds back, and through no fault of his own.
But there was controversy on the final Mont du Chat climb when Froome had a mechanical problem and Aru appeared to break the unwritten rule not to attack the race leader in such a situation. The only other rider within a minute of Froome is Urán, who jumped from 11th to fourth, 55 seconds off the lead.
However, the Briton was able to regain contact as his rivals eased up to wait – in a gesture of fair play praised by Froome later – and began launching a series of attacks that shredded the field. “I think the team is good with that”.
“They have done it before and I’m sure they can do it again”. “When I heard it on the radio, then I stopped”.