The Team Sky man crossed the line first at the summit of La-Pierre-Saint-Martin in the Pyrenees 59 seconds clear of team-mate Richie Porte with Colombian Nairo Quintana (Movistar) third a further five seconds back.
Froome, the 2013 Tour winner, now holds a commanding lead of 2:52 over his closest challenger, Tejay Van Garderen (BMC Racing Team), with Quintana at 3:09.
“I’m at a loss for words,” said Froome afterwards.
“That was unbelievable. I couldn’t believe it when I asked the guys to push hard a little bit and we were hearing on the radio that the big names were getting dropped.
“It was textbook from the team. The guys rode such a good race. I’m over the moon to be able to finish it off for them.”
Albertto Contador was one of the big losers of the day — though there were many more who had their hopes of a podium finish quashed, with the Spaniard admitting he simply had a bad day.
“I didn’t feel great today,” he admitted after. “I couldn’t breathe very well and if you can’t breathe then you can’t feel your legs and as a consequence I couldn’t feel good. It just wasn’t my day today. I usually go well on those sorts of days but it just didn’t go well,” he added.
The 167-kilometre stage was rolling all the way to the start of that vicious final 15-kilometre drag which had an average gradient of 7.4%.
It was Quintana’s Movistar team who dictated the pace early on and the ferocity of their tempo saw several contenders like defending champion Vincenzo Nibali (Astana), Rigoberto Urán (Etixx-QuickStep), Joaquim Rodriguez (Katusha), Thibaut Pinot (FDJ), and Jean-Christophe Péraud (Ag2r La Mondiale) all being dropped.
The front group was already considerably thinned out by the time Team Sky hit the front as the gradients began to kick up.
Yet it was Quintana’s team-mate Alejandro Valverde who was first to fire, with a double dig that appeared to put Froome in difficulty.
But the pre-race favourite didn’t flinch, unlike Contador, Van Garderen, Pierre Rolland (Europcar), Adam Yates (Orica-GreenEdge), and other members of an elite group who began to buckle.
Alone with Quintana and Porte, Froome wasted no time making his move and blazed up the mountainside to take a stranglehold on the yellow jersey and leave the rest of the field in an apparent battle for second place.
Froome’s team-mate Nicolas Roche did some huge turns to whittle down the front group and eventually came over the line 13 minutes back while his cousin Dan Martin fared slightly better, although he lost by over 11 minutes.
It was another gruelling day for Sam Bennett who came home in the last group on the road some 23 minutes down.
Today is another monster stage in the Pyrenees with the riders travelling 188 kilometres from Pau to Cauterets over six categorised climbs.