Valverde (Movistar) dominated the category one climb at the end of the 171km stage from San Roque to Alto Penas Blancas to finish ahead of Bauke Mollema (Trek-Segafredo) , with Rafael Majka (Tinkoff) following in third.
Van Garderen (BMC) was fourth on the stage, 48 seconds back, which forced him to surrender the 22 second lead he had earlier built over his rivals. Mollema's ride was enough to earn him third place overall.
Valverde, who won the race in 2012, 2013 and 2014, started the day 22 seconds down on van Garderen but a well planned attack 7km from the summit at Penas Blancas gave him the buffer.
"It's the most exciting victory of the four I've got here," Valverde said. "It's true that the previous three were also beautiful, but I was feeling like this one was going away from my hands day by day.
"I felt comfortable all stage today, despite the route being so demanding - which also was for me. The team was also doing well and wanted to try and move the race, and we profited from several other teams who wished to go on the attack to make a fast race so we could get a chance to leave Van Garderen back into the last climb.
"We launched several of our guys into the early moves, with Rubén (Fernandez) into a more serious break and Dani (Moreno) in the finale, and when I saw the others struggling a bit halfway through the last Peña Blancas, I knew that I had to go on a long attack if I wanted to win the GC."