Froome and his Sky teammates killed off the hopes of one contender after another, including 2014 winner
As Sky led the way, with three support riders strung out in front of Froome to tug him up the gradients, the lead group shrunk to less than a dozen of the hardiest climbers.
With six kilometers (four miles) to go, on some of the steepest sections, Froome tore away alone, getting out of the saddle as he accelerated. The last rider to stay with him, 2013 runner-up
"Froome has landed a hammer blow on the Tour," said Nibali, the Astana team leader. "I have no more to give. I'm not even the younger brother of the Nibali from last year."
Froome, who was already wearing the race leader's yellow jersey after nine stages, is now nearly three minutes in front.
Closest is still Tejay van Garderen, an American on the BMC team. But he's 2 minutes, 52 seconds behind Froome overall.
Quintana lost more than a minute to Froome on the ascent and is now trailing the British rider by 3:09, in third.
Contador rode in nearly three minutes behind Froome and slipped back to sixth overall, 4:04 behind the leader. Nibali is 6:57 behind Froome in 10th place and looking nothing like the champion who won last year. He lost 4:25 on the climb and was the 21st rider across the line.
"Dream, dream scenario just to hear all those big names being dropped," Froome said. "I couldn't have asked for it to go any better."
Froome also won the first high-mountain stage in 2013 on his way to his first Tour victory. There are still two more climbing days in the Pyrenees, followed by ascents in the Alps.