The Decathlon AG2R La Mondiale rider and Gijs Leemreize attacked from a breakaway group before O'Connor later left the Dutchman behind with 27 kilometres to go.
O'Connor opened up a defendable lead of four minutes 51 seconds in the general classification ahead of veteran Roglic, as the peloton came in well over six minutes down.
"I felt a little bit in my own world today... I just went for it, I felt today was just a day to seize my opportunity and I laid it all out there," O'Connor told Eurosport.
"I felt I could win this stage from the start -- it's pretty special when you can just go out and crush it like that."
O'Connor became the fifth Australian to win stages at all three Grand Tours after winning at the Giro in 2020 and at the Tour de France in 2021.
"I enjoyed today a lot, it was beautiful racing all round," he continued.
"(Wearing red at La Vuelta) is going to be a once in a lifetime experience maybe, so I will enjoy every moment... it's an excellent opportunity and I will savour it as much as I can."
O'Connor finished four minutes 33 seconds ahead of Italian Marco Frigo while Florian Lipowitz came in third, with the German rising to fourth in the general classification.
UAE Team Emirates' Joao Almeida is third overall, trailing Roglic by eight seconds, while defending champion Sepp Kuss languishes six minutes 31 seconds behind new leader O'Connor.
O'Connor finished fourth at the Giro d'Italia this year and also recorded a fourth-place finish at the Tour de France in 2021.
"Yes (it's worrying) because in the end O'Connor isn't just anyone, he took five or six minutes out of us, but at least we had some minutes of advantage," said Almeida.
"It will be hard to take back those minutes... it was very tough, very fast today and very hot, so now we have to recover."
Three riders left the race, Jon Aberasturi, Kenny Elissonde and also Rigoberto Uran, whose team said he suffered a crash.
"He did not finish the stage and is currently being assessed by medical staff," said EF Education-EasyPost on social media.
The stage, which began inside a supermarket, started quickly and the peloton was forced to reel in multiple breakaway attempts.
Eventually a strong group featuring O'Connor and Lipowitz escaped up the road, setting the stage for the Australian's heroics.
Friday's hilly seventh stage takes riders 180.5km from Archidona to Cordoba.
