Rodriguez, 23, pulled off the biggest win of his career by snatching victory in stage 13 at the Vuelta a España, while Jesus Herrada (Cofidis) retained the red jersey but saw his lead significantly trimmed by Simon Yates (Mitchelton-Scott).
Riding his first grand tour and is out of contract with his Euskadi-Murias team, Rodriguez made his mark by freeing himself from a small breakaway group in the final stretch of the summit of the La Camperona mountain, battling against gradients of 24 per cent.
Rodriguez finished 19 seconds ahead of runner-up Rafal Majka (BORA-hansgrohe) and half a minute clear of third-placed Dylan Teuns (BMC).
“I had this stage in my mind but it’s not like I had ticked it," Rodriguez said. "To beat people like Valverde you need to in the break.
"When Majka went in the final climb, I thought I wouldn’t be able to follow him until the top, that it was lost. But then I got closer. When I got back to them (Majka and Teuns), I saw their faces of pain, I went just a bit harder and I went away.
"I’m a rider who suffers from the changes of pace. I figured I’d better climb at my rhythm."
Race leader Herrada struggled in the mountains after going for broke in Thursday's flat stage to lift the red jersey from Yates and his lead was cut down from three minutes 32 seconds at the start of the stage to one minute 42 seconds.
Nairo Quintana finished the strongest of the general classification hopefuls to leapfrog his Movistar teammate Alejandro Valverde into third place, eight seconds behind Yates.
“The whole day has been very fast due to the breakaway," Quintana said. "At the front, there were dangerous people for the general classification.
The leader’s team pulled as they could and then we came to help them with some other teams so the attackers wouldn’t go too far.
"Today was a short explosive finale. There are people better than me for this kind of finales. I’m waiting for longer climbs to open more differences, but every second I win is welcome.
"I hope to keep going like this, with luck and strength. I have good sensations, good legs, and today was a good start. Let’s hope tomorrow and the day after are like this or better.”
The top three Australians are Jack Haig (Mitchelton-Scott), seven minutes off the pace in 21st place. BMC Racing's Rohan Dennis, who won the opening stage, is in 26th place and Jai Hindley (Sunweb) sits in 47th overall.
Stage 14 is a new, 171km route up the Praeres mountain containing five classified climbs and just shy of 3000 metres of vertical climbing, while Sunday sees a visit to Lagos de Covadonga, an old favourite of the Vuelta.