Froome attacked about two-thirds of the way up the mammoth 13-mile Ventoux, and his acceleration was too much for two-time former champion Contador. The Spaniard dropped back and finished about 1 minute, 40 seconds behind.
Colombian Nairo Quintana was second, 29 seconds behind as tens of thousands of people crammed the roadside on Bastille Day France's National Day.
The win means Froome effectively made up the time he lost on Friday's sprint stage, when Contador caught him with a surprise attack. He leads Dutchman Bauke Mollema by 4 minutes, 14 seconds and Contador by 4:25.
The longest stage of the race took riders over 151 miles from Givors in the winemaking Rhone Valley and ended in the Provence region.
Ventoux is one of the most famed climbs in the Tour's 110-year history. Britain's Tom Simpson collapsed and died on it during the 1967 Tour.
Froome raised his right arm in the air when he crossed the line for his second stage win of the race after winning a mountain stage in the Pyrenees on Stage 8 with a similarly decimating attack.
"It was incredible today, incredible. This is the biggest victory of my career," Froome said. "I didn't imagine this, this climb is so historical. It means so much to this race, especially being the 100th edition. I really can't believe this."
A nine-man breakaway group, including sprint champion Peter Sagan and French veteran Sylvain Chavanel, led early in the race. Sagan picked up more valuable points in his quest to win the green jersey for the second straight year, extending his already massive lead over Brit Mark Cavendish, the 2011 Tour sprint champion.
Reputed to be one of cycling's showmen, Sagan lifted his front wheel and did a wheelie, followed by a salute to the crowd in a rare moment of frivolity on an otherwise difficult day.
The small group of front-runners split open on Ventoux, leaving Chavanel alone in front, and with about 9 miles of climbing still to go. Froome, meanwhile, only had two Sky teammates Australian Richie Porte and Britain's Peter Kennaugh to help him.
However, the Movistar team looked full of energy, with Rui Costa of Portugal and Quintana surging ahead.
Quintana had attacked Froome four times on the last climb in the Pyrenean mountains on Stage 9 up to Bagneres-de-Bigorre, but had not been able to beat him.
Quintana zoomed uphill, overtook Jan Bakelants, Chavanel and Spaniard Mikel Nieve to move into the lead with about 6 miles to go, with Nieve tucking in on his wheel. Nieve finished the stage in third spot, 1:23 back.
At this point, Contador still had three teammates with him but Froome would lose Kennaugh shortly after, leaving just Porte.
Then, the yellow jersey group blew wide open as Porte accelerated. Suddenly, Froome and Porte were alone with Contador, whose three teammates Roman Kreuziger, Michael Rogers and Jesus Hernandez drifted back.
Froome appeared to whisper in Porte's ear and with 4 miles to go, Froome launched a devastating attack on Contador rocketing up the slope as fans threw water over him and others lit orange flares or waved British flags close to his face. He was so fast that within moments he had caught Quintana.
As he moved alongside Quintana, Froome attacked again but Quintana responded well.
Other countries were well represented. There were dozens of Union Jacks and Norwegians and Danes wearing Viking costumes. Pockets of Belgians and Dutch swigged beers, others dressed up as animals or ran alongside the riders in inflatable body suits.
The chaotic, raucous, deafeningly loud scene included motorbikes and spectators perilously close to the riders.
Near the summit, the scenery started to change, with fewer and fewer trees; then just a little bit of green brush left, before even that gave way to the barren, lunar landscape that makes Ventoux unique.
Toward the top it was windy, overcast and cool, a welcome respite from the stifling heat below, with temperatures again well into the 90s.
Following a rest day Monday, there is a medium mountain stage on Tuesday 104 miles from the medieval cliff-top town of Vaison-la-Romaine in Provence to Gap in the Alps.
Then come the final few days of agony in the mountains.
There are three straight days of tortuous climbing including two ascents up the famed l'Alpe d'Huez pass in one day on Stage 18. The next two days both feature two Hors Categorie climbs each so tough they are considered beyond classification. The race ends the following day with a nighttime finish on the Champs-Elysees.