Chaves edged out Dutchman Tom Dumoulin in a sprint finish to the 158.7km ride from Alhaurin de la Torre to Caminito del Rey in a time of 3hr 57min 15sec ahead of Ireland’s Nicholas Roche in third.
“It is my first win in a three-week tour. It’s incredible,” said Chaves.
“I hope to hold onto the red jersey (the overall leader) for as long as possible.”
Froome is attempting to become only the third man to win the Tour de France and the Vuelta in the same year.
However, it was Quintana who took an early lead in the battle for the general classification victory as he came in one place ahead of Froome in sixth just 36 seconds behind the leaders.
“I tried to go from far out. It was a climb for explosive riders, I tried but the heat affected me,” said Quintana.
“I saw that Chaves was stronger than those of us in the breakaway, he is a very smart rider and I am happy that one of my compatriots won.”
Another former Grand Tour winner, Vincenzo Nibali, endured a nightmare start as the Italian lost over a minute on Quintana.
The 2014 Tour de France champion had been dropped by the peloton after being caught up in a crash 30 kilometres from the finish before fighting his way back into the main group.
But he was made to pay for the energy he spent in doing so in the category three climb towards the finish line as he finished 1min 38sec back.
“It seems as if this year I have bad luck as I was at the front and we all fell.
“I lost time and thanks to four teammates they carried me back towards the peloton.
“Unfortunately it was a hard climb and I couldn’t give any more. I hope to recover from these injuries on my left side and have a good night’s sleep to start tomorrow’s stage with confidence.”
BMC enjoyed victory on a neutralised team time trial over safety concerns on Saturday, but their leader Tejay Van Garderen, who failed to finish the Tour de France, also lost time on the general classification favourites by finishing 55 seconds behind in 15th. – Agence France-Presse