A tactical masterclass from Contador and his Saxo Bank-Tinkoff team-mates saw the Spaniard take the hilly 187km stage from Santander by six seconds over Alejandro Valvarde (Movistar) and a huge two minutes and 37 seconds over a faltering Rodriguez (Katusha) after a daring attack on the penultimate climb of the day, more than 50 kilometres from the finish.
Contador now leads the race by 1:52 over Valverde while Rodriguez drops to third, 2:28 in arrears.
"A lot of people thought it was crazy to attack from so far away but I knew my form and I had to try," said an emotional Contador after securing his first stage win of the race. "I was not happy being second so I had to go for it," he added, before dedicating his win to "everyone who believed in me - my family, friends, fans and team."
Trailing Rodriguez by 28 seconds on GC following the second rest day, Contador made his bold move on the second of three small climbs, the Cat.2 Collado La Hoz.
The scene was perfectly set for Contador, who had three Saxo Bank team-mates - Bruno Pires, Sergio Paulinho and Jesus Hernandez - riding in a leading group one minute up the road which had formed when two breaks merged on the descent of the previous climb, the Cat.3 Collado de Ozalba.
Contador's surprise attack left both his main rivals for dead, with red jersey Rodriguez and green jersey Valverde caught completely unawares. Wearing the white combined jersey, Contador soon joined the leading group and crossed the summit in pole position with a 20-second lead over his opponents.
What followed was a piece of tactical brilliance from Bjarne Riis's Saxo Bank outfit. Aided by his team-mates, Contador increased the lead to one minute over his two rivals, who rode in a trio in pursuit alongside Rodriguez's Katusha team-mate Alberto Losada.
Both Pires and Hernandez then dropped back to latch on the chasing Rodriguez group, disrupting its rhythm as the gap continued to grow.
In a quite wonderful script, Contador then relied on an old friendship to deliver the fatal blow: joining forces with former Astana team-mate Paolo Tiralongo - for whom Contador gifted a win during last year's Giro d'Italia as a thanks for the Italian's efforts in supporting him in his victorious 2010 Tour campaign - Contador broke clear of the leading group on the approach of the final, gradual Cat.2 climb to the finish.
Having picked up six bonus seconds at the second intermediate sprint, Contador combined with his Astana ally as the gap grew to more than two minutes. With just under 14km to go, Contador dropped Tiralongo and rode solo towards the finish.
Like Contador, Valverde benefited from having bodies in the initial breakaway. First, Valverde was aided by Colombian Nairo Quintana as the pair combined to distance a clearly suffering Rodriguez, who was further isolated after Losada's dropped back. Once Quintana tired, Valverde could rely on another Movistar rider - Benat Intxausti - to continue his pursuit of the lone leader.
Inside the final few kilometres, Valverde and Intxausti caught the remnants of the initial break, including Sergio Henao (Team Sky), Gorka Verdugo (Euskaltel), Rinaldo Nocentini (Ag2R-La Mondiale), Jan Bakelants (RadioShack-Nissan) and that man Tiralongo, the game-changer.
While Contador's advantage over the Valverde group was coming down fast, the 29-year-old's lead over Rodriguez was pushing on three minutes as he passed under the red kite.
Not only was Rodriguez devoid of team support as he pedalled squares to save his race, to add insult to injury he had two of his main rival's team-mates sitting right in his wheel and refusing to co-operate.
After a few nervous looks behind during the closing 500 metres, Contador finally let the emotion get the better of him, roaring with delight and holding both arms aloft as he crossed the line to take perhaps the most significant and symbolic win of his career - and snatch another 12 bonus seconds.
Valverde pipped Henao to take second place (and eight bonus seconds) six seconds in arrears. The 32-year-old's solid fight-back was enough to see him rise to second in the GC at the expense of Rodriguez, who crossed the line 2:38 behind the stage winner and new race leader.
Smiling behind Rodriguez as he stumbled across the finish, Hernandez clenched his fist on the completion of Saxo Bank-Tinkoff's audacious and terrific coup. Rodriguez will take little consolation on being able to wear the green jersey as points leader in Thursday's flat 204.5km stage from Aguilar de Campoo to Valladolid.
"It's a sad day because I lost the Vuelta for sure," said Rodriguez, who came within one stage of winning the Giro d'Italia in May. "No one expected Alberto's attack and sometimes there's no answer to something so spectacular. He won the stage with two balls. But the race is not over and I will try, however difficult."
With just four stages remaining - including Saturday's showpiece stage 20 to Bola del Mundo - Contador is now the man to beat. The 2008 Vuelta champion has never lost his home Tour - and with a lead of 1:52 over Valverde, his new main rival, Contador looks to have secured an historic win on his return to major stage racing following his recent ban.
Any lingering hopes harboured by Britain's Chris Froome of finishing on the podium were dealt a blow when the Team Sky leader finished almost five minutes behind the new red jersey. Last year's runner-up stays in fourth place but is now 9:40 down on GC.