Victory this weekend would make Froome just one of five riders ever to win four or more Tours, and just one short of the all-time record of five, held equally by Eddy Merckx, Jacques Anquetil, Miguel Indurain and Bernard Hinault.
Riding at a leisurely pace far behind them, race leader Chris Froome and other top contenders for the yellow jersey were happy to let others contest the victory on the Tour's longest stage.
Having chewed his way through almost 3,200 kilometers (2,000 miles) of French roads, just three stages now stand between the Briton and top spot on the Champs-Elysees podium in Paris on Sunday night.
Those are the sort of time gaps that can be blown away in a moment on the big mountain stages, and Wednesday's stage 17 to Serre Chevalier certainly qualifies as one of those.
Froome was in no mood to be at the receiving end of another one. Romain Bardet (AG2R La Mondiale) +0:23 3.
"I was hunting for opportunities, and then the roundabout arrived", he said.
The breakaway group split again with 20 kilometers (12 miles) left.
If the peloton had taken a moment to look up during the frantic finish to stage 16, they would have seen the Alps rising up above the finish town as an ominous warning of what is to come next. He ended up 20 seconds ahead of Darwin Atapuma of the United Arab Emirates.
No Frenchman has won the Tour since Bernard Hinault claimed the last of his five titles in 1985.
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"I had a lot hard luck. Luck is now on my side", he said. "I won't take any big risks like in Duesseldorf, but when I can push, I will push". After two energy-sapping days of climbs in the Alps, Froome and his rivals had their sights set instead on the time trial Saturday in Marseille that will determine the podium order before the race ends in Paris on Sunday.
Cavendish, who was watching at home with a fractured shoulder, joined in the celebrations for his team mate who is so often the unsung hero in the Manxman's sprint victories.
In short, Froome is 95 percent of the way there.
"It seems everybody will wait until the last day with the mountain-top finish", said LeMond. "I normally find the Alps more hard".
As a effect, Bardet moved a tiny bit closer to Froome overall, having been 27 seconds behind him at the start of the stage in Briancon. That moved him up to second overall, relegating Rigoberto Uran to third.
"I gave it all, I thought I was going to suffocate as I crossed the line", Bardet said. "I have no regrets, I did everything I could". Bardet and Uran are the only riders within a minute of Froome, after Italian Fabio Aru again faded on that climb and continued his slide down the overall rankings.
Froome was relieved to put the Alps behind him. He is now fifth overall, almost two minutes behind Froome.
Despite the odds stacking in Froome's favor, Bardet isn't ready to concede defeat.
Froome identified Uran as his "biggest threat" in the clock-race and will be watching the Colombian most closely.
Only 22 km realistically stands between Chris Froome and a third consecutive Tour de France triumph but the British rider says he can not rest easy. "But we're in a good position".