The Sky Team rider completed the 37km course between the coastal towns of Javea and Calpe in 46 minutes and 33 seconds to win the 19th stage, his second victory in this year's event.
Quintana (Movistar), wearing the race leader's red jersey, was the last man down the start ramp but could not maintain the pace of the Tour de France winner and finished 11th in the stage, losing two minutes and 16 seconds to Froome.
Alberto Contador (Tinkoff), who finished almost two minutes behind Froome, is now third overall while Esteban Chaves (Orica-Bike Exchange) slipped down to fourth after losing over three minutes.
"Froome was flying," Quintana said. "We still have an advantage and we need to defend it."
Jonathan Castroviejo (Movistar) finished 44 seconds behind Froome and Tobias Ludvigsson (Giant-Alpecin) was third.
"I'm really happy with the result today," Froome said. "Time trials are painful but I get a lot of satisfaction when I'm told I finished first.
"There is one more tough day of racing and let's see what happens."
Froome's hopes of winning a Tour de France and Vuelta double are still alive.
"I love the Vuelta," Froome said.
"It's racing at its toughest and I've really enjoyed it."
Quintana is, however, still favourite to win his first Tour of Spain ahead of Saturday's mountain stage, a 193.2km ride from Benidorm to Alto Aitana before Sunday's sprint finish in Madrid.
"He has more than one minute but we are going to keep on fighting," Froome said.
"We will see what happens tomorrow. Nairo has a good team around him. It's going to be tough to beat him."
How it happened
On a technical course featuring a few smoothly uphill sections, Yves Lampaert (Etixx-Quick Step) set the first reference time in 47min 59sec.
Silvan Dillier (BMC), who was looking to end up among the best, saw his hopes vanish into thin air after a crash in the final u-turn.
Jonathan Castroviejo (Movistar), fourth in the Olympics time trial, lived up to expectations when he clocked 47min 17sec.
At the first intermediate check point, there is already a clear hierarchy between the main favourites. Froome ahead of Contador and Quintana while Chaves was quickly losing time.
Around the halfway point, Froome passed Chaves. The Briton continued to crush the pedals and clocked 31min 08sec at the second intermediate point, leading Contador by 1min 12sec, Quintana by 1min 33sec and Chaves by a massive 2min 14sec.
Meanwhile, Samuel Sanchez (BMC), who was defending his place in the top 10 in GC, crashed and crossed the line far off the pace.
While Froome still has a chance to win the Vuelta, Contador, who is now 3min 43sec behind Quintana, only has a slim hope to win a fourth title.
Chaves is fourth overall 4min 54sec behind while Andrew Talansky(Cannondale-Drapac) is now in the top five at the expense of Simon Yates (Orica-Bike Exchange).