Team Sky boss David Brailsford says that Chris Froome, winner of Wednesday’s Peña Cabarga stage, does not want to finish second overall again in the Vuelta a España and that he is confident he can beat Nairo Quintana (Movistar).

Froome marked Quintana’s attack in the final kilometre of the Peña Cabarga climb this afternoon and on his second acceleration, rode ahead to the stage victory with Quintana on his wheel.

“Chris is now confident he can beat him,” Brailsford said while waiting for his star to arrive at the team bus. “Yeah, Chris doesn’t want to come second here again. It’s all in for the win.”

Quintana maintained the red leader’s jersey by 54 seconds on Froome. His Movistar team-mate Alejandro Valverde is in third at 1-05 minutes and Esteban Chaves (Orica-BikeExchange) sits fourth at 2-34.

Froome has won the Tour de France three times already, so he has experience leading a Grand Tour. He also has experience just missing out in the Vuelta, twice finishing second in 2011 and in 2014.

“From experience, when you’re leading and you have a 54-second lead, it feels like nothing and when you’re chasing that 54 second lead, it seems like quite a lot. It’s funny what it does to you mentally,” Brailsford added. “Whenever you’re leading a Grand Tour you always think that the gap was never big enough and you are never quite comfortable. Nairo doesn’t have that comfort factor.”

Sky won the opening team time trial, but since then Froome has appeared to suffer on some mountain stages while Quintana gained momentum. The stage win on Wednesday, should boost Froome’s confidence with a week and a half to race.

“It lifts his morale and the team’s morale,” said Brailsford. “It gives you that extra bit of energy for the next few days, everything’s just a bit rosier and everybody just feels better. In Chris’s mind, he doesn’t think [Quintana is] unbeatable.”

Froome returned to the place where his Grand Tour star was born on stage 11. In 2011, he dislodged Juan José Cobo to win the Peña Cabarga stage by one second – his first professional and Grand Tour win. It marked him as a future star. Cobo held on to the overall by a slim 13-second lead over Froome and Sky team-mate Bradley Wiggins in third.

“You can never measure the psychological component really, but for sure it was a climb that Chris remembered well. Even when we looked at how we raced it before and he saw himself winning, that was a very positive thing,” Brailsford said.

“Tim [Kerrison] and I were chatting about yesterday when we were out on our bikes. It’s funny how life goes and what happens and the routes that people take. You think, I wonder what would have happened if X or Y had never happened.

“When Chris first came here he was riding for Bradley, who probably wouldn’t have been riding here had he not broke his collarbone [in the Tour]. And the way Bradley smoothed that all was fantastic and I think Chris learned a big lesson there.”