Chris Froome was second in the 160.5-km mountain trek, the Vuelta's 'queen stage', after the Team Sky rider's late acceleration helped the pair drop Spanish duo Alejandro Valverde and Joaquim Rodriguez.
Tinkoff-Saxo rider Contador then powered away with 1.5-km left as he finished 15 seconds ahead of the Briton to tighten his grip on the leader's red jersey.
Froome, who started the day fourth overall, is now only three seconds behind the second-placed Valverde.
Contador leads compatriot Valverde by 1:36 and Froome by 1:39 with Rodriguez fourth, 2:29 off the pace.
"There is reason to be extremely pleased with today's stage but there is still a long way to go," Contador told reporters.
"I knew when to wait for my chance and I was able to widen the gap to all the riders including Froome who kept up an incredible rhythm.
"I was feeling strong, I hung in there, saw my
opportunity and made the most of it. I saw that Purito (Rodriguez) and Valverde were left behind and I knew it was an important day," said Contador.
CHANGES OF PACE
"You cannot take your eye off Froome. Thankfully I was able to keep up with his changes of pace."
Valverde, who refused to cooperate with Contador on Sunday when they could have distanced themselves from a struggling Froome, lost about a minute to the overall leader.
Froome attacked with 4-km to go in the 16.5-km ascent to La Farrapona and only Contador was able to match him.
Valverde and Rodriguez could not follow and had to settle for fourth and fifth position respectively in the stage behind Italy's Alessandro De Marchi, the strongest rider of the day's breakaway.
Italian Gianluca Brambilla and Russian Ivan Rovny traded punches without getting off their bikes and were thrown out of the race.
Local media reported that a Civil Guard motorcyclist was killed when he crashed during the stage.
Froome and Contador opted to ride in the Vuelta after abandoning the Tour de France in July.
The Briton pulled out of the Tour during the fifth stage after crashing while Contador left the race in the 10th leg after breaking his shinbone.
The Spaniard recovered faster than expected and is now looking to win the Vuelta for the third time after prevailing in 2008 and 2012.
Tuesday is the last rest day. The race finishes on Sunday.
(Writing by Julien Pretot, editing by Tony Jimenez)
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