Both overhauled French hope Arnaud Demare of Groupama-FDJ in the final few metres of the 169.5km stage from Bourg d'Oisans.
"When I attacked I was not sure I would be able to keep my advantage".
Thomas has said that although he would work to support Froome, he is not going to intentionally lose time.
The Bahrain team rider was helped back on his bike and, with a courageous effort, rejoined the chase of a small group of stage leaders in a thrilling finale that saw Britain's Geraint Thomas triumph for the second alpine stage in succession.
Unlike on Thursday, when a fan's camera strap appeared to snag Vincenzo Nibali's handlebars on Alpe d'Huez, he slammed to the ground and broke a vertebra.
Thomas said: "I was on his (Nibali) wheel, but I didn't see if he hit a spectator".
Vincenzo Nibali has been forced to withdraw from the Tour de France due to back injuries sustained in a crash on stage 12 of the iconic race.
Stuyven surged ahead alone before the final climb but was passed by Fraile with two kilometres to go. "It was pretty stressful so I had no idea".
Prime Minister to visit Northern Ireland
During her visit, the prime minister is also due to speak to young people in Belfast about Northern Ireland's future. The government's White Paper on Brexit has promised to maintain a frictionless border on the island of Ireland .
I think everyone was happy in the bunch to have a relaxed stage. I don't know. We just train hard, work hard and come here to try to win the race.
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The situation is unusual: an established champion, Chris Froome, with a - faint - question mark over his strength, trailing behind a teammate, Thomas, who pledged to show loyalty, but is in the form of his life and clearly contemplating a career-defining victory.
Prudhomme described the behaviour of some fans as "immoral" as he called for respect.
"We need to restore calm and respect all the riders", he said. Cycling history, from Jacques Anquetil through Eddy Merckx to Bernard Hinault and Lance Armstrong, shows the same truth: the more Grand Tours a rider wins, the better he becomes at finding ways of winning them.
Attitudes toward Froome and his Team Sky soured recently when the four-time Tour champion was involved in an asthma drug case stemming from last year's Spanish Vuelta - even though he was cleared of wrongdoing just days before the Tour started. But at a stroke, it all went up again.
Team Sky are in a position that every one of their rivals in the Tour de France would love.