The veteran bested the younger man in the final metres as an even younger Laurens De Plus (Quick-Step Floors) finished third. Kwiatkowski's efforts were rewarded with the red leader's jersey.
There was Australian fallout on the stage as BMC suffered two general classification casualties with overall leader Rohan Dennis and ill team-mate Richie Porte dropping out of contention after a split in the peloton.
“I’m delighted," Valverde said after his victory. "In the Tour, I didn’t get all the good sensations I was looking for. And now I feel like I have the condition I was looking for.
"It had been some time since I had won a stage at La Vuelta and I wanted to get one, so I’m very happy.
"De Plus went very hard. I calculated the distance and went with 550-600m to go. When we got back to De Plus, I let Kwiatkowski move ahead, and I overcame him in the last curve.
"So far, I’ve achieved the goal of winning a stage and we’ll see how things go day by day.”
The tough 163.5km stage from Marbella to Caminito del Rey featured the requisite break but this one posed some danger with grand tour stage winners Thomas De Gendt (Lotto Soudal) and Pierre Rolland (EF Education First-Drapac) and Alexis Gougeard (AG2R) in the mix along with Pablo Torres (Burgos-BH), Jonathan Lastras (Caja Rural-Seguros RGA), Luis Angel Mate (Cofidis) and Hector Saez (Euskadi-Murias).
Surprisingly De Gendt was the first of the breakaway riders to drop off, his stage ambitions over with 55km to race. The time gap to the peloton was also a casualty after mostly hovering around the four-minute mark but almost cut in half as the road lifted.
With 30km to race and only a minute back to the peloton, Rolland and Gougeard combined to empty the tank, dropping Torres, Lastras, Mate and Saez. Gougeard could not sustain the pace while Rolland was swept up by the peloton 10 kilometres later.
A split in the bunch isolated Dennis and Porte at the worst possible moment but they weren't alone, as Vincenzo Nibali (Bahrain-Merida), still recovering from a Tour de France crash, showed his fitness still needs work, also dropped as a result of the pressure applied by Movistar and Sky.
But they weren't alone, as Vincenzo Nibali (Bahrain-Merida), still recovering from a Tour de France crash, showed his fitness still needs work, dropped as a result of the pressure applied by Movistar and Sky.
From that point, Movistar and Sky engaged in their battle for supremacy, disrupted only for a moment by De Plus who charged to the finish from a kilometre and a half out.
Valverde made the first move to bridge across to De Plus forcing a reaction from Kwiatkowski who joined in the two-man uphill sprint to the finish.
The crafty Valverde then forced Kwiatkowski to the front before coming off his wheel to add yet another stage win to his career tally, his 120th.