Team Jayco–AlUla's Dunbar spent much of the 166.5 kilometre route in a breakaway pack, suffering on the sharp hills with everyone else, only bursting clear 600 metres from the line in Padron.
Known as a climber, it was a surprise move from the 27-year-old Corkman and his rivals failed to pick him up until it was too late, allowing him to take his first ever stage victory in a grand tour.
"It's been a while since I've been in a scenario like this, if I'm honest," Dunbar told Eurosport at the finish.
"I just kind of used my experience. I was suffering a bit on that steep climb, then I realised everyone else was.
"I just played my cards. I said I'd gamble and back my finish. I know on a finish like this after a hard race I can sprint but I knew I had to go long.
"Going from 600 to go was probably a bit long for a sprint but it was what I had to do to win. I can't believe it."
Quinten Hermans (Alpecin-Deceuninck) and Max Poole (Team dsm-firmenich PostNL) followed him across the line two seconds behind to complete the stage podium.
O'Connor started the day three minutes 53 seconds ahead of Roglic but the Australian wilted as Roglic turned the screw on the final punishing climb up the category three Puerto Cruzeiras.
He crossed the line 37sec behind Roglic, still 3min 16sec in front but badly wounded psychologically on a bruising day.
The win marks a significant turnaround for the popular Dunbar who left Ineos Grenadiers in 2023 to become a GC contender.
He finished seventh at last year's Giro d'Italia but failed to finish the Vuelta.
This year, he crashed in the Giro in May and suffered a cruciate ligament injury that he feared might have signalled the end of his career.
"Since the Vuelta last year, I think I've had seven or eight crashes," said Dunbar.
"Physically it takes its toll but mentally it took its toll on me too.
"I said numerous times in my head that I might not have a future in the sport because of the crashes and injuries that I've had.
"This year, after the Giro, when I injured my ACL, I thought that would be the nail in the coffin for my cycling career.
"But I have incredible support around me. My girlfriend is always there for me and I have an incredible group of family and friends, and the team backed me so much.
"It's been a long time coming but to repay them all today means a lot."
