Only an accident or other freak mishap on Sunday's largely ceremonial final ride to Paris could stop Froome from winning the 100th Tour.
Froome finished third in a dramatic Stage 20 to the ski station of Annecy-Semnoz in the Alps that decided the other podium placings.
Nairo Quintana from Colombia won the stage and moved up to second overall.
Joaquim Rodriguez from Spain rode in 17 seconds behind Quintana. He moved up to third overall.
Froome's lead is more than five minutes over both those two.
Alberto Contador, who had been second at the start of the day, struggled on the final climb and dropped off the podium.
The 125-kilometre trek was the last of four successive stages in the Alps and the final significant obstacle Froome needed to overcome before Sunday's usually relaxed ride to the finish on the Champs-Elysees in Paris. That 133-kilometre jaunt starts in Versailles.
Froome's dominance at this Tour was such that this victory could very well be the first of several. At 28, he is entering peak years for a bike racer. He proved at this Tour that he excels both in climbs and time trials — skills essential for those who want to win cycling's premier race. He also handled with poise and aplomb questions about doping in cycling and suspicions about the strength of his own performances. He insisted that he raced clean.
Froome first took the race lead and the yellow jersey that goes with it on Stage 8, when he won the climb to the Ax-3 Domaines ski station in the Pyrenees. On Sunday's Stage 21, he will wear the yellow jersey for the 13th straight day.
Froome told French television that when he passed the sign showing 2 kilometres to go on Saturday's final climb, "for the first time I realized that it was almost won."
"It was hard today," he said. "Rodriguez and Quintana raced very strongly."
Sunday "will be a day for sprinters on the Champs-Elysees. For us, it is done."
Saturday's stage did a big loop south of Annecy, through the mountains of Savoie between the lakes of Annecy and Bourget. This is cheese-making country, with lush Alpine pastures and dense, naturally cool forests.
Quintana's win also secured him the spotted jersey awarded to riders who pick up the most points on mountain climbs. He also retained the white jersey as the Tour's best young rider. He wiped away tears in his news conference as stage winner.
"I couldn't ask for more," he said. "I got nearly everything. It was fabulous."
"It's a very special day in Colombia. A big party and the whole of Colombia is celebrating."
Unlike on Friday, when storms drenched the pack, the sun shone and the skies were blue on Sataurday. When a motorbike-borne television camera focused on Spanish rider Alejandro Valverde, he motioned that riding in such conditions was hot, tiring work.
The ride took the racers up six climbs. The last two of those were particularly tough. The last steep climb to Annecy-Semnoz, past ski lifts and ski slopes, was rated HC or "Hors Categorie", meaning it's considered too hard to classify.
It was the last really tough climb of this Tour. The riders have just two small humps to climb on their leisurely Sunday ride from the Versailles Palace to the Champs-Elysees' cobbles, where sprinters including Mark Cavendish will battle for the stage win.
Uniquely for the 100th Tour, Stage 21 will set off in the late afternoon, so the race finishes more or less as the sun is setting behind the Arc de Triomphe.
For a chunk of Saturday, the race was led by its oldest rider, Jens Voigt. The 41-year-old German was part of a group of 10 riders that broke away fromn the pack early in the stage.
"Since I'm almost sure that this was my last Tour, I wanted to say a proper goodbye," said Voigt.
"I gave eveything," he said. "I'm happy and now it is over for me."
He was caught in the battle on the final climb. Quintana, Froome and Rodriguez rode off, leaving Contador to labour behind. The winner of 2007 and '09 who was stripped of his 2010 victory and banned for a failed doping test ran out of legs.
Contador placed 7th in the stage, coming in more than 2 minutes behind Quintana.
That dropped him to 4th overall, more than seven minutes back from Froome.
Canada's Ryder Hesjedal is 69th overall after finishing the stage in 85th. David Veilleux of Cap-Rouge, Que., is 122nd overall while Svein Tuft of Langley, B.C., is last at 170th.