Britain's Team Sky rider Froome struggled on the special category climb to Alto de los Machucos, with Italy's Vincenzo Nibali cutting his overall lead by 42 seconds to 1:16.
Veteran Spanish rider Alberto Contador came in second, clawing back more than a minute on Froome to keep alive the race for the red jersey, after the Briton's impressive time-trial performance on Tuesday seemed to have ended it.
Aqua Blue Sport rider Denifl beat Contador by 28 seconds on the 180.5-km run from Villadiego to Los Machucos in dangerous, misty conditions with limited visibility.
Froome remained confident of Vuelta victory despite the disappointing stage, in which he was unable to respond to attacks by Trek-Segafredo rider Contador and third-placed Miguel Angel Lopez.
"It's still a great position to be in," Froome, who placed 14th in the stage, told reporters. "It was a really tough final (climb), especially with the weather conditions. It was a typical Vuelta summit finish, and the same for everyone.
"I don't think anybody enjoys gradients over 25 percent. It's never nice to lose time but I'm confident we can get the job done."
Denifl had been part of the initial breakaway and the triumphant rider said it was the finest day of his career.
"For my team, Aqua Blue, we're at our first Vuelta here, and winning a stage, it's just amazing, I'm over the moon," he said. "It's the best day in my cycling life."
(Reporting by Rik Sharma; Editing by Ken Ferris and Clare Fallon)
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