The 40-year-old veteran showed he still has what it takes after he latched on to an early breakaway before attacking in the final hour as part of a final bunch of five that would go on to contest the stage win.
The Movistar rider's third-place finish helped the Spaniard gain 57 seconds in the general classification battle.
Movistar now has three riders in the top 10, with Mas in fifth at 1:07 and Marc Soler 35 seconds down on him in seventh. Valverde is in ninth, 2:03 down on red jersey Richard Carapaz
“The team was good today,” said Valverde’s teammate Enric Mas.
“Valverde did today a ’10’ and couldn’t win just due to the circumstances of the race.
“We can play three cards in the GC, especially in the hard stages that will decide this Vuelta.
“It’s a huge benefit to us to have three of us within range of victory.”
The 2009 Vuelta winner has had an up and down start to this year's race with a fifth-place finish on stage two his previous best result.
Despite pushing hard for the stage win, Valverde was caught out by eventual winner Michael Woods' late attack.
“I wanted to win but everybody in the break was watching my wheel the closest, and that makes it harder," he said.
“I let one of the guys in the break out of my sight and that was some guy I let do that.”
“I was up there in a possible support role, too, to see if any of my teammates (Mas and Soler) bridged across from the main group.”
“This year’s Vuelta is all out every day.
“And it offers lots of opportunities. We’ll try to make the most of them.”
An 11km mountaintop finish up the steep pitches of Alro del Moncalvillo during Thursday's (AEDT) 164km stage will sure to test Valverde and his Movistar team as they step up their pursuit for the winners red jersey.