Yates, who had won Saturday's stage to snatch back the red jersey, increased his overall lead over Alejandro Valverde from 20 to 26 seconds.
He finished two seconds ahead of the Spaniard and collected four bonus seconds for coming third on the 178.2km route from Ribera de Arriba to Lagos de Covadonga, a third consecutive summit finish.
Yates also widened the gap to 2016 champion Nairo Quintana in third to 33 seconds by beating the Colombian to the finish line by four seconds.
He was, however, seen arguing with Quintana, who did not help him chase down Miguel Angel Lopez, who finished second, two seconds ahead of Yates.
Yates had arrived at the foot of the final climb in good form after being shepherded in a combined slipstream of his Mitchelton-Scott team mates and Astana.
He had plenty of energy to launch a series of attacks in the clouds of the Lagos de Covadonga mountain to counter the efforts of Valverde and Quintana.
There was little he could do to catch up with Pinot, however, who avenged his bold yet futile solo attack on stage 11 by storming to a fourth individual grand tour stage victory by an impressive 28 seconds.
Pinot was part of a small breakaway involving Enric Mas, Valverde, Steven Kruijswijk and Lopez but this time carefully picked his moment, freeing himself from the group with six kilometres remaining and slowly increasing the gap to the chasing pack.
Monday is the second and final rest day of the race, which starts again with an individual time trial on Tuesday and concludes on Sunday with a procession through Madrid after one flat stage and three further summit finishes.
(Reporting by Richard Martin; Editing by Toby Davis)
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