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Team DSM's rising star Storer launched an attack on the final 4km of the ascent on the Puerto de Almachar to free himself from the chasing group.
He never looked back, descending comfortably to collect his second stage win of this Vuelta, finishing 22 seconds ahead of Mauri Vansevenant in second and Clement Champoussin in third.
Storer became only the second Australian to win two stages in a Vuelta edition, after Michael Matthews in 2013.
He had also dominated in the climb to win the seventh stage.
"It's even more unbelievable than the last time," Storer said.
"There was a massive fight for the breakaway. It was one of those epic days where it took more than 80 kilometres before it went. I was happy to get in there and then I was feeling good on the last climb, and I knew exactly what I needed to do on the last climb – I needed to attack.
"I didn't have exact time gaps, but I knew it was tight. I knew I had to go fast down the descent even though it had the dry and slippery road of this region. I was happy with my descent. It was just enough to hold on.
"I dreamt of one stage at this Vuelta and now I have two after 10 days. It's truly unbelievable."
As Storer descended to victory, the red jersey battle erupted once more on the climb at 12 minutes down. Roglič flew away from his rivals on the way up, keen to put even more time between him and his GC rivals.
The Slovenian was too strong for his rivals on the climb and appeared to stretch his lead of the race even further before misjudging a corner and sliding out across the road.
While he got back up within seconds, it wasn't quick enough as the podium-contending chase group of Movistar's Enric Mas and Miguel Angel López and Jack Haig (Bahrain Victorious) joined him, with the quartet rolling home 11:49 behind Storer.
Intermarché-Wanty-Gobert Matériaux's Odd Christian Eiking did enough to take the Maillot Rojo after being 9:10 down at the start of the day
Eiking now leads the race by 58 seconds from fellow breakaway rider Guillaume Martin (Cofidis). The Norwegian came home fifth on the day, part of the chase group. Roglič, meanwhile, lies in third place 2:17 down.
