A mountainous day in the saddle came to a thrilling climax at the summit finish as the top climbers in this year's Vuelta a Espana tackled the imposing slopes of the Mas de la Costa climb, a four-kilometre climb at 12.3 per cent average gradient.
Attacks by Quintana on the final climb softened up the competition and reduced the race down to just a select group of four, with Valverde, Primoz Roglic (Jumbo-Visma) and Miguel Angel Lopez (Astana) joining the Movistar pair at the front of the race.
Quintana set the tempo for his team-mate when it became clear he wasn't able to get away and Valverde unleashed his trademark furious acceleration at the finish to take the win just ahead of Roglic, with Quintana and Lopez finishing six seconds adrift.
"I'm so, so happy," said Valverde. "This season has already been good to me, always up there within the best, but taking a stage like this one in La Vuelta, with such a strong competition - it really makes me happy.
"I want to thank all of my team-mates for the huge gamble they made on us for the win, and Nairo in particular, because he rode brilliantly over the last climb. He tried to distance Roglic and López with his attacks, but seeing they were able to match him, he set a steady pace so I could go for the victory later on.
"I was confident, I knew I was doing well, and the worst result I could have got was fourth! I just tried to keep the moves under control, and I knew I was the fastest of the three, so I remained calm until the end."
The final ascent assault came after the early breakaway of the day had been neutralised by a peloton keen not for the breakaway to make it two consecutive stage victories.
Young Australian Michael Storer (Team Sunweb) was in the early move, along with Jelle Wallays (Lotto Soudal), Philippe Gilbert (Deceuninck-QuickStep), Sergio Henao (UAE Team Emirates), Stéphane Rossetto (Cofidis), Quentin Jauregui (AG2R La Mondiale), Gianluca Brambilla (Trek-Segafredo) and Sebastian Henao (Team Ineos).
Together they established a healthy lead over the peloton in the opening kilometres but despite a maximum advantage of five minutes at one point the chances of the break winning the day again were always low.
Overnight leader Dylan Teuns (Bahrain Merida) cracked completely with 26 kilometres to go and lost nearly ten minutes on the stage where Valverde, Quintana, Roglic and Lopez proved that they are the strongest riders in this year’s race.
Valverde's win helped him jump to third overall after almost a week of racing, with Lopez taking back the leader's jersey again, the third time he has taken or re-taken the lead in what has been a dynamic Vuelta to date.
