The 10th stage followed Monday's punishing cobbled ride to Roubaix and Tuesday's rest day and, with a long descent to the finish, none of the top guns was in the mood to risk a long-range attack.
Julian Alaphilippe claimed France's first victory on this year's Tour when he climbed impressively to win the 158.5-kilometre ride from Annecy to Le Grand Bornand.
The Quick-Step Floors rider crossed the line to an exuberant reception from the French fans.
Belgiuan Greg van Avermaet was part of the breakaway group with Alaphilippe and finished fourth to maintain his grip on the yellow jersey.
Spaniard Ion Izagirre and Estonian Rein Taaramae finished second and third, respectively.
"I did not expect this; it's incredible,'' the 26-year-old Alaphilippe said after his first win on the Tour.
Van Avermaet leads Briton Geraint Thomas, Froome's lieutenant at Team Sky, by 2min 22sec.
Spaniard Alejandro Valverde is third, 3min 10sec off the pace, with Froome in sixth place, 3min 21sec behind Van Avermaet, who said he had "zero chance'' of keeping the yellow jersey after this morning's brutal mountain stage to La Rosiere.
For Froome, the 158.5-km trek from Annecy was one day ticked off his to-do list as the Briton remained in a perfect position to become the first rider in 20 years to achieve a Giro d'Italia-Tour de France double.
"We couldn't have asked for much more, really. It was pretty steady,'' Froome, whose climbing abilities should do the talking in the coming days, said.
A final time trial on the eve of the Champs Elysees parade should also help him gain time on his rivals, with the exception of Dutchman Tom Dumoulin, who is 3min 42sec off the pace in 11th.
"We were pretty happy to have the numbers up front. For the first big mountain day I think the guys really showed exactly what we've been training for,'' Froome added.
"I'm feeling pretty good.''
Among Froome's rivals, the Movistar team - with potential winners in Valverde, Nairo Quintana and Mikel Landa -did not even try to unsettle the four-time champion in another demonstration of its conservative tactics.
"Everyone's got their own game lan. Other people are probably also thinking about these next hard days coming up,'' Froome said.
"No-one really showed all their cards today. Everyone I think played it a little conservatively maybe thinking about the next two days to come, which are going to be hard as well.''
Dumoulin, the 2017 Giro champion, refused to see the day as a lost opportunity to shake Team Sky, the dominant force in the peloton.
"It's only the first mountain stage,'' he said.
That stage, however, was disastrous for last year's runner-up, Colombian Rigoberto Uran, who lost more than 2min just two days after losing ground following a crash on the cobbles.
"He's pretty sore after crashing two times on the cobbles,'' his EF Education First-Drapac sports director Charly Wegelius said. `
`He did what he could to limit the damage but unfortunately it's the way sport goes. It's a brutal sport.''
