The 20-year-old Pogacar win the short explosive 94.4km stage from Andorra la Vella to Cortals d'Encamp after an intense weather affected battle which started 19km from the finish.
“It’s just incredible. I was looking for my opportunity. Yesterday, when I looked at the weather, I was happy with the rain forecast," Pogačar said.
"I tried to follow the attacks. Then I went full gas in the gravel section and in the end, it just went perfect. Today was a tricky stage. It’s incredible to win ahead of such champions.”
Quintana is six seconds ahead of Primoz Roglic (Jumbo-Visma) and Miguel Angel Lopez (Astana) is third at 17 seconds.
The Colombian climber leads the Vuelta for the first time since 2016 when he won the race overall.
"Team orders were given for Marc Soler to wait and help me out," Quintana said. "He did stop and pulled for as long as he could or wanted to.
"As for me, I kept moving forward as I was trying to edge out my rivals as much as possible. The stages in Andorra are always quite hard, also because of the weather. It rained less than expected, but the hail made us go through a lot of misery.”
It looked as if Lopez would take the stage and overall lead with a 35 seconds gap to his key rivals but the lights went out when a storm struck and when the TV signal returned Movistar's Quintana and Alejandro Valverde had bridged while Roglic followed at 15 seconds.
With less than five kilometres left and the classification battle in full play, Movistar's Marc Soler took the lead in an effort to set up Quintana for the win.
Clearly the strongest and with a Vuelta stage win in sight, an upset Soler was ordered to wait for Quintana who then bridged across with Pogacar in tow.
Movistar's well-played plans were scuppered when the young Slovenian attacked leaving Quintana to take second while Roglis finished fast for third on the stage.
The Vuelta resumes racing with a 36.2km time trial from Jurancon to Pau in France on SBS Viceland LIVE from 2300 AEST.
"Let’s see how the ITT pans out," Quintana said. "It’s likely I’ll lose La Roja against better time triallist such as Primoz Roglic or my teammate Alejandro Valverde.
"Anyway, I’m sure I’ll do a good performance, as being the leader on the GC is quite motivating. I’ve been getting better since Mas de la Costa, and I’m sure I’ll improve further from today on."