The defending champion made his surprise move after the final climb of the eighth stage, bursting clear over the top and then powering downhill to cross the line alone after 184-km from Pau to Bagneres-de-Luchon.
His main challengers for overall honors, including Colombian Nairo Quintana, could not keep pace, trailing him by 13 seconds at the finish.
Two-time champion Alberto Contador of Spain had already dropped back on the last climb as his challenge faded away.
Froome received a 10-second time bonus for his victory to take over as race leader from Belgium's Greg Van Avarmaet, who had been in yellow for three days.
Fellow Briton Adam Yates finished in the 13-strong chasing group to take over in second overall behind the Team Sky rider.
British riders hold three of the four major jerseys, with Froome in yellow, Mark Cavendish in green after his three stage wins and Yates in white as best young rider.
It was a sixth Tour de France stage win for Froome, who is well-placed to add to his overall wins in 2013 and 2015.
Renowned as a climber, his daredevil descent came as a surprise to all.
"It wasn't really planned. I thought I'd give it a try in the downhill as the few tries on the climb didn't work out," he told the official Tour de France website.
"So I decided to give it a go in the descent. It was cool.
"Tomorrow is a hard stage but I take every second I can. It's just a really good feeling to win," he added.
Sky team principal Dave Brailsford was delighted for his star rider. "He takes opportunities when he can. Everyone thinks about him going uphill, not down," he told the Press Association..
"Everyone says we're predictable so we said this year let's be unpredictable and make people guess what we're going to do."
Sunday sees another big day in the Pyrenees, 184.5-km from Vielha Val d'Aran to Andorre Arcalis and the first mountain top finish, with Froome and Movistar's Quintana, sixth at 23 seconds, set for another showdown.