Nairo Quintana, champion in 2016, looked set to take the red jersey from Jesus Herrada as well as the stage victory as he charged ahead with fellow Colombian Miguel Angel Lopez on his tail towards the top of the Les Praeres mountain.
Yates, however, bided his time before attacking in the brief flat section of the final climb just as the final kilometre approached, closing in on the Colombians then surging ahead as the climb kicked in on the 171km route from Cistierna to Les Praeres de Nava.
Mitchelton-Scott rider Yates finished two seconds ahead of Lopez and Spaniard Alejandro Valverde and seven seconds clear of fifth-placed Quintana, retaking the red jersey after ceding it to Spaniard Herrada on Thursday.
Yates holds an overall 20-second lead over 2009 winner Valverde and 25 over Quintana, with Lopez 47 seconds back in fourth.
"I chose my moment really well and didn't look back until it flattened out a little. There was a bit of a gap, so I just gave everything to the line," said Yates, who first took the red jersey after coming ninth in stage nine but only had a one-second advantage over Valverde then.
"I'm much happier now, I feel I deserve it more this time. I gave everything I could," he added.
Valverde, meanwhile, said the new route for the stage affected his decision making.
"In the end it (the stage win) escaped my grasp, it's a shame I didn't know the climb, I thought the final part was harder than it was and when I wanted to put the pressure on it was too late," said the Spaniard.
Herrada was rarely considered as a serious contender in the general classification and after seeing his lead significantly trimmed on Friday, he suffered even more on the second consecutive summit finish, finishing nine minutes and 16 seconds behind Yates.
Herrada tumbled down to 17th in the general classification, seven minutes 44 seconds back from the Briton.
Sunday's stage 15 is the third consecutive summit finish, a 178.2km route from Ribera de Arriba to Lagos de Covadonga, a mountain which has proved decisive in determining the Vuelta winner on several occasions and where Quintana triumphed on the way to his overall victory in 2016.
"Today was a difficult day with very complicated descents and a finale as explosive as this one didn't benefit me," Quintana said.
"Sometimes you have to go for it and risk a bullet. Sometimes it comes off, other times you feel like you are shooting into thin air.
"Tomorrow is a different type of climb, a different battle that suits me better than today's."
(Reporting by Richard Martin, editing by Pritha Sarkar)
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