BMC's Cummings attacked from a breakaway of seven riders with three kilometres remaining of the rolling 173km stage from Santiago de Compostela and, despite the best efforts of fellow escapees Cameron Meyer (Orica-GreenEdge) and Juan Antonio Flecha (Team Sky), Cummings held on for the win.
Green jersey John Degenkolb (Argos-Shimano) led the peloton over the line 40 seconds in arrears as Spaniard Joaquim Rodriguez (Katusha) retained his 13-second lead over Alberto Contador (Saxo Bank-Tinkoff) in the general classification ahead of three consecutive days in the Asturias mountains.
Victory for 31-year-old Cummings was a remarkable turnaround for a rider whose season took a huge blow in February when an accident in the Tour of the Algarve saw Cummings break his pelvis.
Cummings recovered in time to support defending champion Cadel Evans in July's Tour de France - but it was a bittersweet return, with the Australian failing to retain his crown and Cummings finishing the race as the only British rider without a stage victory to his name, following wins for Team Sky trio Mark Cavendish, Bradley Wiggins and Chris Froome, and Garmin-Sharp's David Millar.
"It's been a difficult year but this is the best win of my career," said an ecstatic Cummings. "I would like to thank by BMC team for all the support they have shown through the hard times. The whole day was hard and in the end I played it really well. For me to win, I knew I had to do it alone because there were some fast people in the group. So I made my move and then all I could do was go full gas, 100 per cent."
Cummings, a former team-mate of Froome at Barloworld and Wiggins at Team Sky, was part of a seven-man break that formed after an opening 50km of frenetic riding in Galicia, north-west Spain.
Following numerous thwarted breakaway attempts - including one from a 24-strong group of riders - the day's decisive break built up a cushion of three minutes over the peloton, which was being controlled by the Argos-Shimano team of Degenkolb.
With the German youngster in search of his fifth stage win on the race, Argos-Shimano made sure the advantage of the seven leaders never increased to more than three-and-a-half minutes. But with no rider a threat on GC, the Dutch team received no hope from the strong Katusha, Movistar and Saxo Bank teams of the Spanish race favourites.
The presence of Italian sprinter Elia Viviani and Spanish veteran Flecha in the break meant both Liquigas and Team Sky refused to co-operate, while the withdrawal of French sprinter Nacer Bouhanni mid-way through the stage - owing to a knee injury picked up in a crash in Thursday's stage 12 - saw FDJ-BigMat also take a back seat.
To make matters worse for the chasing peloton, half of the Lotto Belisol team of sprinters Gianni Meersman and Vicente Reynes was suffering from a virus - while the Orica-GreenEdge team of sprinter Allan Davis had two men in the break: Meyer and stage four winner Simon Clarke.
With such a intricate scenario playing out, the break - which also included Germany's Linus Gerdemann (RadioShack) and Belgian Thomas de Gendt (Vacansoleil) - managed to defy the peloton until the very end.
Argos-Shimano combined well to reduce the gap to 58 seconds entering the final 20km - but soon Degenkolb was left on his own after what appeared to be a complete burnout from his team-mates.
Strong winds while crossing a bridge over the bay near the industrial port of Ferriol brought about a few splits in the peloton while three riders - Dani Moreno (Katusha), Gert Steegmans (Omega Pharma-QuickStep) and Andrey Kashechkin (Astana) - disrupted the chase by trying to counter attack inside the final 8km.
With the peloton in disarray but still just 40 seconds behind, Flecha made the first move from the break. The Spaniard broke clear with 6km remaining but was foiled by Cummings. Viviani was dropped off the back as the other escapees caught up with the two leaders with 4km to go - but Cummings then made his decisive move just over 3km from the finish.
Meyer and Flecha led the chase and at one point looked to be closing in on the lone leader. But Cummings - using his track background - dug deep and time trialled himself to a memorable and unlikely victory, punching the air in celebration before raising both arms aloft as he crossed the line.
Meyer took second place ahead of Flecha, four seconds back, while Clarke led Gerdemann and de Gendt over the line a further 10 seconds back.
Degenkolb pipped Australia's Davis for seventh-place as the peloton came home 40 seconds behind Cummings.
There was no change in the overall standings amongst the race favourites. Rodriguez leads Contador by 13 seconds and Froome by 51 seconds ahead of three successive mountain-top finishes that could decide the race. Alejandro Valverde (Movistar) completes the 'Big Four', 1:20 behind his compatriot 'Purito'.
The Vuelta continues on Saturday with the 149km stage 14 which includes five categorised climbs including the gruelling finish atop the Puerto de Ancares.