Orica rider Chaves, who surrendered first place to Dumoulin (Giant) on Wednesday, attacked around two kilometres before the steep finish into Sierra de Cazorla and despite the searing heat had enough in the tank to hold off Daniel Martin (Cannondale) and Dumoulin, who crossed the line together five seconds behind.
Chaves heads the general classification by 10 seconds from Dumoulin, with Irish cousins Martin (+33 seconds) and Nicolas Roche (Team Sky, +36) in third and fourth respectively.
"I can’t believe I’ve won," Chaves told reporters.
"It was a long, hot, hard stage today," he added. " I’m really happy and I want to thank all the team and staff again, they’re all amazing."
Sky leader Chris Froome, who won a second Tour de France crown in July and is bidding for a rare Tour-Vuelta double, finished seventh and moved up one place to sixth overall (+55).
Friday's summit finish on the seventh stage into La Alpujarra is expected to provide one of the first genuine skirmishes among the race favourites.
Briton Froome is bunched with some of his main rivals including Spaniards Alejandro Valverde (Movistar, +49) and Joaquim Rodriguez (Katusha, +56) and Valverde's Colombian team mate Nairo Quintana (+57).
Orica's Daryl Impey said the Australian outfit, whose young rider Caleb Ewan won Wednesday's fifth stage, were having a much better time at the Vuelta than in last month's Tour de France, where things had not gone to plan.
"That’s cycling and sports in general, you have your ups and downs and this is fantastic," Impey told reporters.
"I think he (Chaves) is just in great condition at the moment and when you’ve got good condition it seems like he can’t do anything wrong," added the South African.
Frenchmen Jacques Anquetil (1963) and Bernard Hinault (1978) are the only riders to have won the Tour and the Vuelta in the same year.
(Reporting by Iain Rogers, editing by Alan Baldwin)
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