Set up by Australian team-mate Richie Porte, who eventually finished second, Froome launched his winning move with only Nairo Quintana (Movistar) able to mount an initial resistance.
In contrast none of Froome’s rivals looked particularly impressive. Vincenzo Nibali (Astana) was the first to be dropped, then Alberto Contador (Tinkoff-Saxo) and Tejay van Garderen (BMC).
Froome now leads van Garderen by 2min 52sec, with Quintana a further 17 seconds in arrears.
Pierrick Fédrigo (Bretagne-Séché) fired the first shot with a solo breakaway before he was joined by Kenneth van Bilsen (Cofidis). The pair settled into a massive lead of more than 14 minutes before the peloton began to react.
The leading pair ran through three mountains classifications and one intermediate sprint together before the peloton began to reel them back in on the 15.3-kilometre long climb of La Pierre-Saint-Martin.
Fédrigo and Bilsen hit the climb with two minutes in hand but that was quickly eroded by a fast moving peloton which was rapidly dropping riders like Mark Cavendish (Etixx-QuickStep) Australian Rohan Dennis (BMC) and former world road champion Rui Costa (Lampre-Merida).
The Movistar team of Nairo Quintana took command at the front as Team Sky held its fire with a strategy of reacting to proceedings rather than animating the stage.
Robert Gesink (LottoNL-Jumbo) was the first of the quality climbers to make a move and was shortly joined by Rafael Valls (Lampre-Merida) but defending champion Nibali was immediately in trouble as he tailed off the back of an increasingly select group.
Movistar’s Alejandro Valverde probed the strength of Froome and Sky but was unable to put up a sustained resistance to the Sky juggernaut. Froome waited until only he, Quintana and Porte were left at the front of the race and with one attack instantly gapped Quintana to take an iron grip on the yellow jersey.
Quintana ground away in second but was passed by Porte with only metres remaining. Gesink finished in fourth to cap off his best performance in several years and is now in eighth place overall.
Van Garderen finished 2min 30sec down to retain his second place on the general classificatoin, while Contador completed the stage 2min 51sec down and sixth on GC, more than four minutes back. Nibali finished a lowly 21st on the stage, 4min 25sec down, effectively ending his title defence.
"When I heard the big names were struggling and getting dropped, I told Richie Porte and Geraint Thomas 'let's push'," Froome said after the stage.
"I could feel our rivals were in trouble after the rest day so my teammates set up the finale for me. I attacked when it was steep before the road was flatting out. It's the dream scenario. I couldn't have asked for any better one, especially with Richie coming second and taking the time bonus away from Quintana."