Evenepoel blasted out of a breakaway group on the first of two climbs of the Puerto de La Cruz de Linares late in the 179-kilometre ride from Pola de Allande and was in a class of his own.
The peloton, featuring the Jumbo-Visma trio of Kuss, Jonas Vingegaard (26) and Primoz Roglic (33) finished nearly 10 minutes back with Kuss emerging still in the maillot rojo after surviving the last big day in the mountains.
American Kuss, who was shepherded through the dramatic Asturian landscape by his illustrious teammates, even extended his lead over Tour de France champion Vingegaard to 17 seconds and is just over one minute ahead of Giro d'Italia champion Roglic.
With a flat stage on Friday followed by a demanding penultimate stage on Saturday, Kuss is now favourite to retain the red jersey all the way to Madrid.
With the Jumbo-Visma trio well clear of field, the dominant Dutch outfit look certain to become the first team to win all three Grand Tours in the same season, a feat made even more impressive given it will be with three separate riders.
Evenepoel's hopes of fighting the Jumbo-Visma riders for the overall title evaporated on stage 13 when he was dropped on the Col d'Aubisque and lost 27 minutes.
But the 2022 champion has bounced back in stunning fashion by winning stage 14 and now soloing to victory on Thursday for what was the 50th professional win of his career.
"The legs were super good today and I was the strongest in the breakaway group so I just had to go for it today," Evenepoel told Eurosport after wrapping up the king of the mountains title. "It was an amazing stage to win again."
He finished four minutes and 44 seconds ahead of Italy's Damiano Caruso (35, Bahrain Victorious) and 5:10 ahead of Denmark's Andreas Kron (25, Lotto Dstny) who came third.
"It was a super good opportunity to take the points for my jersey - I took all the points - and my third stage win is amazing to end the Vuelta with."
Kuss had looked vulnerable to attacks from his own team mates in the past week but the American now has Vingegaard and Roglic effectively working for him with both of them appearing more than happy to do so.
He even put in a late kick to cover an acceleration by fourth-placed overall Juan Ayuso (21, UAE Team Emirates) and Enric Mas (28, Movistar) to open up a bigger gap on Vingegaard.
Provided he avoids any mishaps on Friday and Saturday, Kuss will be a popular champion in Madrid.
Vingegaard, who has been helped often by Kuss, warned that there is still a tough stage on Saturday and that the team needed to keep fighting.
"It's sure nice to be able to pay Sepp back," the Dane said. "He has done so much for me and Primoz. Saturday is a tough long stage though so we have to be careful."
