Rodriguez survived a medley of attacks from his main rival Alberto Contador on the ridiculously steep final climb of the 184km stage from Gijon to Valgrande-Pajares, taking third place and some vital bonus seconds behind stage winner Cataldo and second-place Thomas de Gendt of Belgium.
Katusha captain Rodriguez now leads Saxo Bank-Tinkoff's Contador by 28 seconds on GC with another Spaniard, Alejandro Valverde of Movistar, in third place, two minutes and four seconds in arrears.
Britain's Chris Froome, runner up in last year's Vuelta, cracked on the brutal final climb of Cuitu Negru and is now almost five minutes behind red jersey Rodriguez ahead of the race's second rest day.
Billed as the Vuelta's 'queen stage', Monday's race certainly lived up to the hype - concluding with a final section so steep that it looked as if the riders were climbing in slow motion.
Omega Pharma-Quick Step's Cataldo and de Gendt of Vacansoleil-DCM had broken clear of the peloton on the descent of the first climb of the day, the Cat.3 Alto de la Cabrunana, around 50km into the stage.
Combining well, Cataldo and de Gendt - both more than an hour down on GC - built up a maximum lead of 15 minutes over the peloton ahead of the first of two back-to-back Cat.1 climbs. The leading duo crossed the summit of the Puerto de San Lorenzo with a lead of 13:10 over the peloton and looked odds-on to contest the final win.
There was little action from the peloton on the penultimate climb of the day, the Alto de la Cobertoria, where Saxo Bank marshalled matters while the race's big three riders - Rodriguez, Contador and Valverde - rode well off the pace towards the back of the main pack.
A group of six riders broke clear on the descent under the instigation of Luis Angel Mate (Cofidis) and Maxime Bouet (Ag2r-La Mondiale) but they were swept up before the final climb of the day, the HC ascent to Valgrande-Pajares which, for the first time in Vuelta history, was being topped with a new Cuitu Negru 'super-climb' - a 2.8km paved goat track with sections as high as 25 percent.
Cataldo and de Gendt still held an advantage of more than eight minutes as Saxo Bank set a pulsating tempo on the front of the peloton, which was soon whittled down to less than 20 riders.
Unknowing of the drama unfolding behind them, the leading duo pressed on towards the summit. Having secured third place in May's Giro d'Italia by winning the race's 'queen stage' atop the Stelvio, 25-year-old de Gendt seemed to be the favourite to take the victory.
But it was Cataldo who dropped his opponent inside the final 2km when the slopes hit a series of perilously steep ramps. De Gendt did his best to fight back onto his rival's wheel, but Cataldo, his face a picture of pain, managed to hold on for the win. Punching the air, the 27-year-old Italian crossed the line seven seconds ahead of de Gendt to take the biggest win of his career - and a first for his team on this year's Vuelta.
Despite being pipped for the win, de Gendt had crossed the two preceding Cat.1 summits in pole position and rises to third on the king of the mountains classification, five points behind Australian Simon Clarke (Orica-GreenEdge).
Meanwhile, further down the mountain, a flurry of blistering attacks from Contador had seen the whole field - including, most notably, Froome - dropped. Red race leader Rodriguez managed to cover every attack put in by his main rival in white, while green jersey Valverde constantly fought back with the help of his Movistar team-mate Nairo Quintana.
Valverde was distanced on the steepest section of the Cuitu Negru ramp - but managed to ride back onto the wheels of his opponents just as Contador put in one final last-ditch dig inside the final 500 metres.
This time, Rodriguez not only held on but managed to pass Contador, sprinting clear of his rival to secure the four bonus seconds for third place. Rodriguez crossed the line of what was quite possibly the most arduous finish ever seen on the Vuelta 2:39 down on winner Cataldo and two seconds ahead of Contador. Valverde was fifth, 17 seconds back, while Colombian Quintana took sixth place.
Froome finished 5:11 down on stage winner Cataldo in 14th place and is now 4:52 behind Rodriguez on GC in fourth place.
With just five stages remaining - including Saturday's showdown summit finish at Bolo del Mundo - it looks all but certain that the 67th edition of the Vuelta a Espana will conclude in Madrid on Sunday with three Spaniards on the podium. But with just 28 seconds separating Rodriguez and Contador, there is still everything left to play for in the battle for the red jersey.
The Vuelta continues on Wednesday with the rolling 187km stage 17, concluding with a Cat.2 climb to Fuente De.