Yates lost significant ground in the race as a result of the crash and Steve Cummings, the Dimension Data rider, went on to win the stage.
Belgian Greg van Avermaet was fifth to extend his yellow jersey lead.
Defending champion Chris Froome finished safely alongside his main rivals despite an inflatable arch collapsing on the road with less than half a mile left.
Yates, 23, also earned the white jersey as the tour’s highest-placed young rider after officials took the finishing times about 2 miles from the end of the 101-mile leg from L’Isle-Jourdain to Lac de Payolle. “We will try to penalise as few people as possible by recording the time gaps when the riders went through that three-kilometre check, they won’t be massive because it was downhill to the finish from there”.
The Aspin, which was included in the Tour for the 73rd time, was affronted from its longer southern slope, 12 kilometers at an average gradient of 6.5 percent.
“They tried to put me in the best position at the foot of the climb”, said Pinot, who enjoyed a strong start to the season crowned by a time trial title at the French national championships last month.
The stage ended in farcical fashion when the inflatable arch marking one km to go deflated and slowed down the bunch, sending Briton Adam Yates to the ground.
Daryl Impey of South Africa finished second and Daniel Navarro of Spain crossed third, each 65 seconds behind Cummings.
Cummings, who won a stage past year, said: “I’m ecstatic for the team – it was a brilliant day”.
In the overall, Van Avermaet leads Julian Alaphilippe of France by 6:36, with Alejandro Valverde of Spain third, 6:38 back. “After two kilometers, I understood I was not in top form”.
It represents the best start to a Tour for Cavendish, who has moved on to 29 Tour stage victories, second all-time to Eddy Merckx’s 34.
Once the 11 hit the Col d’Aspin, Nibali attacked with only Impey and Navarro keeping his wheel, while in the peloton Pinot’s FDJ team set the pace, a decision he would perhaps later regret.
Yates underlined that his main goal is winning one of the mountain stages not the yellow jersey.
Van Avermaet actually extended his overall lead; none of the serious GC contenders were willing to chase him, knowing that Saturday’s and Sunday’s stages will be exponentially more hard and decisive. The eighth stage covers four passes including the Tourmalet and Peyresourde before it finishes in finishes in Bagnères-de-Luchon.