The Quick-Step rider beat his main rival Spaniard Enric Mas of Movistar on the climb to the summit of Piornal on the mountains of Extremadura with Dutch veteran Robert Gesink of Jumbo-Visma trailing in third.
Evenepoel extended his overall lead on Mas to two minutes and seven seconds at the end of a stage marked by numerous attacks.
It was the second stage victory on this year's Vuelta for Evenepoel after his success in the individual time-trial between Elche and Alicante on stage 10.
An accident at the start of the day caused the leader of the climbers' classification, Australian Jay Vine, to retire and seriously affected Spaniard Carlos Rodriguez, fifth overall, who managed to finish the stage.
Ecuadorian Richard Carapaz will pull on the blue polka dot jersey on Friday, a mid-mountain stage around Talavera de la Reina, which will include two second-category climbs at the Pielago pass.
