Quintana looked like he wanted to let rip on the final climb but the Colombian said the finish wasn't for him.
"Today was a short explosive finale. There are people better than me for this kind of finales," he explained. "I’m waiting for longer climbs to open more differences, but every second I win is welcome."
Although he put a couple of seconds into Yates, the dynamic duo fought largely toe-to-toe.
"It was a bit of a drag race with Nairo, we were just sprinting next to each other until the flatter section," Yates said.
"There was a bit of a stalemate until I attacked just before one kilometre to go. We had a bit of a gap and started looking to each other for who was going to take control before we had a bit of a sprint to the line, and he put me away there by a few seconds.
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“It was a good day for me and the team, the first day of the ‘big weekend’. Some guys are showing some weakness, of course they can always bounce back but the GC is really starting to take shape.”
One rider not showing weakness, despite a 20 second loss, is Astana's Miguel Ángel López. He clawed his way back to the main GC bunch after suffering a late mechanical and despite the time loss, jumped three places to sit just behind Alejandro Valverde.
"On a steep part in the final I got a mechanical and had to stop," he said. "Fortunately, I was able to solve the problem by myself, because our car was far away. But, of course, I lost time. I had to spend a lot of energy to come back in the group.
"So, when Quintana and Yates attacked I just had no power to answer since I did not recover after my chasing the group. In the end of the day I lost 20 seconds… It is a lot, but I will keep on fighting."
Rigoberto Uran also improved his place overall and now sits sixth just behind López. After a cracking Vuelta so far, Dimension Data's Ben King also finds himself in the overall top 15 as Fabio Aru (UAE Emirates) slipped just outside.
1. Jesús Herrada (Cofidis)
2. Simon Yates (Mitchelton-Scott) +1:42
3. Nairo Quintana (Movistar) +1:50
4. Alejandro Valverde (Movistar) +1:54
5. Miguel Angel Lopez (Astana) +2:23
6. Rigoberto Uran (EF Drapac) +2:33
7. Ion Izagirre (Bahrain Merida) +2:35
8. Tony Gallopin (AG2R Mondiale) +2:40
9. Steven Kruijswijk (LottoNL Jumbo) +2:44
10. Emanuel Buchmann (Bora-hansgrohe) +2:47
11. Enric Mas (Quick-Step Floors) +3:00
12. David De La Cruz (Sky) +3:34
13. Wilco Kelderman (Sunweb) +3:51
14. George Bennett (LottoNL-Jumbo) +3:53
15. Ben King (Dimension Data) +4:10