After attacking where the single-track road looped its way up a mist-enshrouded cliffside, the Geox rider gained 48 seconds on Dutchman Wout Poels and Russia’s Denis Menchov.
Nicknamed “the Bison,” Cobo crossed the finish line on desolate moorland waving the little finger and thumb of his right hand like bison horns as a victory gesture.
Overnight leader Bradley Wiggins of Britain received strong assistance from Sky team mate Chris Froome but suffered on ramp-like slopes that rose over 23 percent in places.
With six stages left, Cobo leads by 20 seconds from Froome, with Wiggins now third overall at 46 seconds.
Cobo, 30, said he had planned a later attack but had opted to charge away when he saw the rest of the field were suffering.
“It was a long way from the finish on such a steep climb, but I felt very good,” he told reporters.
“Over the radio my directors kept on telling me to stay calm and that I would have a chance.
“For sure this is the biggest victory of my career.”
Cobo, who suffered from depression for the first six months of the year and had even thought of giving up racing altogether, reaped the rewards of sticking with his sport.
“I finally turned things around with the support of the team,” he said. “It was a difficult time but this is the reward for my perseverance.”
Cobo, 10th in the Vuelta in 2009 when he won a mountain stage in the sierras of Madrid, was not at all confident he could hold on to win the race which finishes on Sept. 11.
“Sky are second and third overall and I’m sure this isn’t the end of the road for them,” he said.
“There’s a steep mountain top finish next Wednesday and then two hard stages in the Basque Country. It’s not over yet.”
