Sky team mates Gianni Moscon and Mikel Nieve were again critical to Froome's success as the peloton caught the break on the final climb of the 174km flat stage in Alicante province in punishing heat.
Froome held off a late attack from nearest challenger Esteban Chaves (Orica-Scott) while leaving Alberto Contador (Trek-Segafredo) behind, 12 seconds adrift.
Michael Woods finished five seconds behind Froome in third after a strong display from his Cannondale-Drapac team, who learnt on Saturday that their future is up in the air as they struggle to find a sponsor for next season.
"I put everything I had into that last couple of hundred metres. I was determined that they weren't going to catch me," Froome said.
"I’m really, really happy to get the victory. The team did a brilliant job on that final climb and set such a good tempo. After a week we couldn’t have asked to be in a better position. It’s been a fantastic start to the Vuelta.
"The legs are feeling great. I’ve been to the Vuelta so many times, trying to target this race, and so far it feels like everything is going really well."
The four-times Tour de France champion finished four seconds ahead of Chaves to extend his hold on the red jersey from 28 seconds to 36.