Fellow Spaniard Alejandro Valverde still leads with a one second advantage over American Chris Horner followed by Rodriguez at 34 seconds.
Rodriguez staged a surprise lone attack as the favorites were preparing to tackle the main challenge of the day, the short but painfully steep Alto de Aia-Fronton climb.
Already the outright winner of the Tour of Catalunya two weeks ago, the 30-year-old Spaniard then soloed to his third victory of the season with a 14 second advantage over compatriot Samuel Sanchez. Valverde was third.
"I went for a long-range attack because I thought that way I'd catch everybody out," Rodriguez told reporters.
"I'd lost time in yesterday's stage because I didn't feel good for no real reason and I wasn't happy about it." "I wracked my brains about how best to put it right and I was still feeling pretty gloomy before today's stage started." "Getting a better position overall wasn't the day's big objective, all I wanted was to reach the line first and be able to put my hands in the air." Race leader and Caisse D'Epargne rider Valverde said his former teammate's strategy was exceptionally well planned.
"You can never rule Joaquim out of the fight, he had one card to play and he played it well," Valverde said. "Fortunately we managed to pull him back but it was a very dangerous move." On a tough 170km stage featuring a succession of narrow, twisting lanes and punchy, steep climbs 13 riders gave up while others were forced to dismount on the 26 percent (1 in 4) slopes of the daunting Alto de Aia-Fronton ascent.
Spaniard Amets Txurruka crashed whilst leading when his bike span out of control on a fast downhill section and he suffered a suspected broken collarbone.
Leading in the King of the Mountains competition, Txurruka completed the stage 36 minutes and 20 seconds behind Rodriguez.
Team mate Alan Perez stood in for the injured Euskaltel-Euskadi rider in the post-race ceremonies.
With eight riders clustered at a minute or less overall behind leader Valverde, Saturday's final 22km individual time trial in Orio will decide the race's overall winner.
"It's an extremely technical course and there will be some big time gaps," said Valverde. "Whoever wins won't have it easy."
