Jumbo-Visma rider Kuss, usually a domestique for star teammates Jonas Vingegaard and Primoz Roglic, was helped by the more illustrious duo to hold on to his slender lead on the last major mountain stage of this Vuelta.
The Dutch team seem to have decided that Kuss should win a Grand Tour for the first time, after he took the general classification lead and held it from stage eight onwards.
The slender climb specialist Kuss increased his lead on second-placed Vingegaard by nine seconds after the back-to-back Tour de France winner eased up in the finale to leave the American with a 17-second advantage atop the overall standings.
Third is three-time Vuelta winner and Giro d'Italia champion Roglic, one minute and eight seconds behind Kuss, with Jumbo-Visma set to become the first team to win all three Grand Tours in a single year.
Soudal-QuickStep rider Evenepoel, who finished four minutes 44 seconds ahead of second-placed Damiano Caruso, recorded his 50th career victory.
The tricky 179-kilometre run in Asturias from Pola de Allande to La Cruz de Linares with five classified climbs promised excitement.
A strong early breakaway roared off ahead, including Evenepoel, who has clinched the blue and white jersey for the Vuelta's best climber.
The reigning champion eventually dropped most of the break with Caruso and 20-year-old Max Poole sticking with him for a while.
Evenepoel, whose Grand Tour defence collapsed last week on Tourmalet, has been reborn since and captured his third stage win on Thursday - nobody has more.
The Belgian tapped his head as he headed to the line in the Vuelta's final mountain finish as he also assured the King of the Mountains jersey.
"I felt I was the strongest of the group and I didn't have to waste any time and I just had to go for it," said Evenepoel.
"After my bad day on Tourmalet I just had to turn the page and go for the stages."
In Friday's flat stage 19, riders travel 177.5 kilometres from La Baneza to Iscar, with a bunch sprint to the finish expected.
The 78th edition of the Vuelta ends on Sunday in Madrid after 21 stages and 3,153.8 kilometres, having begun in Barcelona.
