Briton Yates won from the day's breakaway, three days after his first stage victory in the southwestern mountain range.
Coming right after the ascent of the Tourmalet – where Pinot had already showed his great form and stamina with a stage win at the famed Tour mountain – stage 15 ran close to the ancient Cathar castles and was a punishing ride totalling more than 39 kilometres of climbing.
Yates, the Vuelta defending champion, made his decisive move about 9 kilometres from the line.
"I'm very proud of that," Yates said of his second victory at this Tour.
Thibaut Pinot crossed the finish line in second place, 33 seconds behind Yates, and moved to fourth overall, with his attack seven kilometres from the finish blowing away the favourites' group.
Alaphilippe was isolated without a single teammate, and cracked in the final of the four climbs. He managed to retain his overall lead, but defending champion Geraint Thomas, who also struggled, recovered to take almost half a minute off the yellow jersey.
The Frenchman was so exhausted after his effort up the hill, where he grimaced through the rain, that he had to grip a roadside barrier afterward while he caught his breath.
"If I crack I hope he'll carry the torch for the French," Alaphilippe said about Pinot.
Before Monday's rest day, Alaphilippe leads Thomas by 1:35, Dutchman Steven Kruijswijk by 1:47 and Pinot by 1:50.
(with AFP, Reuters)