Kuss attacked from sizeable lead group on the brutal climb to the Observatorio Astrofisico de Javalambre at the end of the 183km ride from La Vall D'Aixo and blasted to victory.
France's Lenny Martinez (20, Groupama-FDJ) finished 26 seconds back from Kuss in second place to move into the overall leader's red jersey.
Back down the road Jumbo Visma's race favourites Primoz Roglic (34) and Jonas Vingegaard (26) took the chance to attack Evenepoel on the steep final slopes, finishing 30 seconds ahead of the Belgian who dug deep to limit his losses.
Belgium's Evenepoel had said before the stage that he would be happy to give up the red jersey on the stage, but what he did not want to do was lose time to his GC rivals.
An unpredictable stage saw a huge breakaway group featuring multiple riders from the powerhouse teams with several close enough on the overall standings to take the red jersey.
The race splintered on the 11.9km climb to the finish featuring gradients of up to 16%, but Kuss roared up towards the summit to grab a victory that took the limelight away from his Jumbo Visma team mates Roglic and Vingegaard.
"It was an incredibly hard stage and we wanted to try and go in the break," Kuss said. "The whole day I felt super good and was just thinking about when to go."
While Kuss is ostensibly working for his two illustrious teammates, he now finds himself in second place overall, only eight seconds behind Martinez.
Spain's Marc Soler (29, UAE Team Emirates) is third overall, 51 seconds off the lead, after finishing fifth on the stage.
Evenepoel has dropped to ninth, two minutes 47 seconds behind Martinez but of more concern will that he now leads Tour de France winner Vingegaard by only five seconds and Roglic by 11 seconds with some massive mountain days ahead.
"If this was a bad day then it's okay," Evenepoel said. "I started to feel a bit heavy-legged but let's hope this is one of the worst days for me."
