Spain’s former two-time winner Alberto Contador was unable to respond when Froome spun away from a small group of riders having seen many of them drop off the pace.
Having started the 242.5km 15th stage 2min 48secs down on Froome, Contador finished in sixth at 1:40 to drop to 4:25 behind the leader and 11secs adrift of second-placed Dutchman Bauke Mollema.
It is Froome’s fourth career stage win on the race and second of the 100th edition after his victory atop Ax-Trois-Domaines in the Pyrenees on last Sunday’s eighth stage.
“It’s a mythic climb. It’s the biggest win of my career,” said Froome, who needed oxygen at the finish to help him breathe. “It was my aim today to take as much time as possible for the GC (general classification).”
On what was the longest stage of the race, expectations were high that Froome’s Sky team, having lost two key riders in recent days, would come under attack from a number of teams chasing various goals in the race.
Sky, however, put the setback of losing Vasili Kiryienka and Edvald Boasson Hagen behind them on their way towards placing Froome in the perfect position thanks to a long spell of fast pace-setting.
A nine-man breakaway had escaped and as none were a threat to the leader, they were allowed to build a lead of seven minutes on the chasing bunch.
The last of that group, Frenchman Sylvain Chavanel, was caught halfway up the 20.8km trek to the Ventoux summit and after some speculative attacks, Froome’s leading group began to thin in dramatic fashion.
Former champion Andy Schleck struggled to keep pace and rode into a ditch while 2011 winner Cadel Evans was next to feel the effects of the fast pace.
After Sky’s Pete Kennaugh’s pace-setting job was over, Porte began his relay with 9.5km to race and the Australian’s efforts did the most damage.
Dutch climbing specialist Robert Gesink and Spain’s Alejandro Valverde were next to feel the pace.
Soon, Mollema and Belkin teammate Laurens ten Dam were left behind as Froome followed Porte’s wheel with Contador keeping a tight rein.
When Froome’s attack came, it was spectacular, the Kenyan-born Briton spinning away from his Spanish rival. He caught Quintana with 6.7km to race and after testing the Colombian again rode away for good in the final two kilometres.
“I didn’t think I’d win the stage,” added Froome. “I thought Quintana would. But at the end he lost his legs a bit and so I just raced on ahead.”