Pinot (Groupama-FDJ) attacked Yates (Mitchelton-Scott) at the end of the 154 kilometre climb from Lleida in Catalonia to Andorra's Naturlandia to take the win.
“La Vuelta was already a success on Sunday (after the victory at Lagos de Covadonga)," Pinot said. "I had come without pressure. I didn’t have the general classification in my mind, I wanted to win stages.
"The first victory, it was already very good. And now, two victories, it allows me to hammer it down. It’s a dream Vuelta. I wanted to enjoy myself and I proved I was able to win head to head with the strongest climbers.
"I had ticked those two stages. Today, the climb was longer and not as steep, it suited my abilities better. And I enjoyed a strong ascent from Simon Yates to go get the victory. He proved he was the strongest today.”
Yates, who is now a small step away from general classification victory, stormed to the front with 10km to go, increasing the gap on Movistar's veteran Valverde.
With Movistar keeping a tight leash on the peloton it took 80 kilometres of riding before a break was established when Benjamin Thomas (Groupama-FDJ) and Jonathan Castroviejo (Sky) received some leeway before they were caught just before the final climb.
There was some hope for the general classification contenders when a split in the peloton, initiated by Movistar, briefly distanced Yates but the team reacted to bring the red jersey back to the front before a showdown on the 17 kilometre long Coll de la Rabassa.
Nairo Quintana (Movistar) attacked with 13km to go before LottoNL-Jumbo duo Steven Kruijswijk and George Bennett followed. Pinot (Groupama-FDJ) joined them with 12km to go before Yates bridged across on his own with 10km to go.
Yates then set a hard pace with Quintana the first to be dropped with eight kilometres left to the summit.
With Kruijswijk and George Bennett also dropped, Pinot and Yates worked together at the front and opened a one minute gap over the chasing group containing the struggling Valverde.
“I haven’t won La Vuelta yet. I’m very wary of tomorrow," Yates said. "We saw today what can happen in just one day. I'll try to stay focused now.
"Of course I enjoyed today but it’s not over until it’s over. I felt good which is why I tried. The team did a fantastic job again. Jack (Haig) did a good ride to really set me up before I went away and Adam (Yates) was always behind in case they came back.
"I have to thank Thibaut (Pinot) for helping me. He could have easily sat on. He was here for the stage win but he could have stayed behind and not help. Chapeau and… You don’t forget things like that very fast.”
The Mitchelton-Scott rider holds a one minute and 38 second lead over Valverde ahead of a decisive Stage 20 in Andorra, which features 4000m of climbing. Kruijswijk is back on the podium, 20 seconds behind Valverde.
La Vuelta a Espana continues tomorrow with Stage 20 in the mountains with a trip from Escalades-Engordany to Collada de la Gallina.