Movistar’s Valverde put a disappointing Tour de France behind him by holding off race leader Kwiatkowski in the final 50 metres of the 163.5km second stage from Marbella to Caminito del Rey.
“I had an extremely difficult Tour de France and I didn’t have all the sensations I wanted,” Valverde told Eurosport after delighting the home fans.
“So I was basically training hard to make it for La Vuelta. Thankfully our plan succeeded and I’m really happy to take this victory because I just couldn’t have done it any earlier.
“I calculated really well the distance to go and just tried to keep something back for the finish.”
An early attack saw a seven-strong group break away from the peloton but that was down to two, Alexis Gougeard (AG2R-La Mondiale) and Pierre Rolland (Education First-Drapac), with 20km to go.
The pair were gradually reeled in and Valverde showed his strength to out-sprint Kwiatkowski, with Laurens De Plus (Quick-Step Floors) finishing third, three seconds back.
Time trial winner Rohan Dennis (BMC) had a difficult day, suffering an early puncture before being dropped with 17km to go as the pace intensified.
Kwiatkowski, the Pole who finished second in Saturday’s opening time-trial, holds a 14-second advantage over Valverde heading into Monday’s 178.2km stage between Mijas and Alhaurin de la Torre.
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