The Mitchelton-Scott Brit leads by 1-38 minutes on Valverde. He gained over a minute on stage 19 on Friday, leaving behind Valverde on the Rabassa summit finish.
"It's clear that it's now more difficult to get that red jersey than it was this morning but we mustn't roll over," Valverde said when reaching the top.
Yates jumped from a 25-second lead just when Movistar seemed to be cooking up a plan for Valverde further down the climb. His Movistar team-mate Nairo Quintana went free at 13 kilometres out with Steven Kruijswijk (LottoNL-Jumbo) and later Thibaut Pinot (Groupama-FDJ).
Valverde seemed to be lacking the kick he had in the past mountain days. The 38-year-old 2009 Vuelta winner is not giving up, however, with one mountain day to race.
"What happened to me today could happen to him tomorrow," Valverde said. "It'll be difficult [to win the Vuelta], of course. It was difficult this morning, it's difficult now. But it's not impossible. We're going to try, clearly."
A massive chance for Movistar to try is on the menu tomorrow. The Vuelta's final mountain stage covers 97.3 kilometres with six categorised climbs. The action starts immediately with an unmarked climb and continues to the end with the Gallina summit finish.
"Can Yates be beaten? I don't know," Valverde added.
"Tomorrow we might take time back or we might lose more. Who knows."
Jack Haig rode tempo for Yates when Quintana attacked. When Haig pulled off, Yates still had brother Adam Yates with him. He did not wait for Valverde to make a move first.
Richard Carapaz pulled for the first part of the climb. Movistar forced splits earlier before the climb and seemed to be ready to launch similar moves on the Rabassa. Once Yates went, and without Carapaz, Quintana returned to help Valverde. However, neither Quintana nor Valverde had the strength of Yates.
Valverde shrugged and said, "Unfortunately the body doesn't always respond the same way."
Thank you for reading 20 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1