Trailing Saxo Bank-Tinkoff's Contador in the closing moments of the fearsome Cat.1 climb, Katusha's Rodriguez clawed his way back to pass his main rival inside the final 500 metres of an action-packed stage to take a thrilling victory and another handful of seconds to cement his place at the top of the overall standings.
Rodriguez now leads Contador by 22 seconds on GC with third place Chris Froome (Team Sky) dropping to one minute and 41 seconds off the pace after the Briton came home 38 seconds down on Rodriguez and behind Spaniards Alejandro Valverde (Movistar) and Daniel Moreno (Katusha).
On the first of three back-to-back mountain-top finishes, Rodriguez underlined his credentials as race favourite with a remarkable triumph in the face of adversity.
Contador's Saxo Bank team had controlled the whole of the 149km stage from Palas de Rei, allowing a 16-man group off the front of the peloton ahead of the first of five categorised climbs before sweeping up the escapees on the final climb of the day.
Surrounded by five team-mates for the final two Cat.1 ascents, Contador looked in control of the situation as the Spaniard attempted to win his first stage of the race and move into the red jersey.
A puncture for Contador on the penultimate climb - the Cat.1 Alto de Folgueiras de Aigas - slightly disrupted Saxo Bank's supreme pace-setting as the main pack crossed the summit 1:40 down on the leading group, which had been whittled down to 10 riders.
Australia's Simon Clarke (Orica-GreenEdge) came out on top of his duel with fellow escapee David Moncoutie (Cofidis), picking up maximum points over three summits to move back into the lead of the mountains classification and thwart the French veteran's bid to win a historic fifth successive KOM title.
Katusha's Alberto Losada attacked from the break on the rolling ride into the final climb of the day, the Spaniard holding an advantage of 1:50 as he started the final Puerto de Ancares ascent.
With Saxo Bank setting a fierce pace on the front, the remnants of the break were soon reeled in - while Rabobank GC hopes Robert Gesink and Bauke Mollema were both instantaneously dropped on the demanding climb (9.5km long at an average gradient of 8.1%).
Set up by two team-mates, Contador - wearing the white combined jersey - launched a blistering attack with 3.5km remaining as lone rider Losada rode 25 seconds further up the unsealed road.
Movistar's Valverde and Katusha pair Rodriguez and Moreno managed to latch on to Contador's wheel, but a faltering Froome was distanced.
With 2km to go, the tempo slowed as Losada was swept up by the main protagonists, while Froome being paced back by Colombian team-mate Rigoberto Uran alongside the American Andrew Talansky (Garmin-Sharp).
Contador then stepped on the pedals with an almighty dig with 2km to go, dropping his rivals for dead and opening up a comfortable lead.
Froome then turned the stage on its head by not only catching Rodriguez, Valverde and Moreno, but passing the Spanish trio and riding off in solo pursuit of Contador.
But it proved the last throw of the dice for last year's Vuelta runner-up and Froome was caught and spat out by Valverde and Rodriguez with one kilometre to go.
Rodriguez in turn shed Valverde and rode back onto the wheel of Contador, who grimaced and put in a last-ditch attack with 200 metres remaining. Rodriguez proved way too strong, however, and jumped out of the saddle to pass his rival with apparent ease to cross the line five seconds clear.
Valverde took third place, 13 seconds down, before Moreno made it a Spanish top-four when he overtook Froome in the closing straight to take fourth place, 35 seconds behind his Katusha team-mate.
Froome and Valverde are now both 1:41 down on Rodriguez on GC in third and fourth respectively. Moreno rises to fifth, 4:16 in arrears, after Dutchman Gesink conceded almost two minutes on the race's first major mountains test.
Talansky impressed with a solid sixth place to ride to eightH on GC, while another top 10 for Nicolas Roche (Ag2R-La Mondiale) saw the Irishman retain his seventh place on GC behind Gesink.
"It's a good start to these decisive stages but there's still some very tough days in the mountains to come and with 90 seconds lead, it can all go wrong very easily," Rodriguez told reporters.
"Alberto's attacks are really dangerous, really spectacular, I suffered like anything to stay on his wheel.
"But I saw that Valverde was closing the gap and I knew I had to go for it again."
Asked if his performance on Saturday proved that he could succeed on the mountains, he replied: "I don't know why there have ever been any doubts, somebody out there is obsessed with that idea. Losing to someone like Alberto or Froome on the big climbs is no disgrace."
Contador, who hugged Rodriguez after crossing the finishing line, added: "I knew that if it came down to the two of us in the last kilometre, Joaquim would win.
"I've got three hard days in the mountains left to try and beat him. This isn't over yet."
The Vuelta continues on Sunday with the 186.5km stage 15 from La Robla to Lagos de Covadonga, which features three climbs ahead of another tough Cat.1 finish.