The Briton had support from Sky team mates Gianni Moscon and Mikel Nieve as the peloton caught up with the breakaway in the final climb of the 174km flat stage in Alicante province in punishing heat.
He darted ahead of Nieve in the final kilometres, holding off a late attack from nearest challenger Esteban Chaves while leaving Spaniard Alberto Contador behind, 12 seconds adrift.
"I put everything I had into that last couple of hundred metres. I was determined that they weren't going to catch me," Froome told reporters.
"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 over the Colombian and further boost his chances of becoming the first rider to do a Vuelta-Tour double since 1978.
Canada's 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.
(Reporting by Richard Martin, Editing by Ed Osmond)
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