University of Alabama student Dunne - whose coach Alan Murray is also his caddie this week - is the first amateur since the legendary Bobby Jones to lead The Open after 54 holes, the American going on to lift the Claret Jug at St Andrews in 1927.
Three years later, Jones became the last amateur winner of The Open to date at Royal Liverpool and went on to complete the "Impregnable Quadrilateral" of Amateur Championship, Open Championship, US Open and US Amateur titles.
Dunne, who came through final qualifying at Woburn for the second year running, was in the second group out on Thursday and joked after birdies on the first two holes that he hoped someone had taken a screenshot to prove he had led the Open.
Three days later he had no such worries and could turn his attention from trying to win the silver medal for leading amateur to the Claret Jug.
"I don't see why not," said Dunne, who is 80th in the world amateur rankings. "I mean, I'm well capable of shooting the scores that I need to win if everyone else doesn't play their best.
"Whether it happens or not, I can't really control. I can just go out and try to play my game and see where it leaves me at the end of the day. Hopefully I play great again and post a good number.
It's surreal I'm leading The Open, but I can easily believe that I shot the three scores that I shot. - Dunne
"If we were playing an amateur event here, I wouldn't be too surprised by the scores I shot. It's just lucky that it happens to be in the biggest event in the world!
"Hopefully I can do it again tomorrow, but whether I do or not, I'll survive either way."
Spieth is looking to become the first player to win the first three Majors of the year and just the third to win any three in a single season - Ben Hogan won the Masters and US Open in 1953 but missed the US PGA to compete in, and win, the following week's Open at Carnoustie, while Tiger Woods won the US Open, Open and US PGA in 2000 and completed the 'Tiger Slam' in the 2001 Masters.
"It hasn't come up in my head while I've been playing yet," said the 21 year old, who would also replace Rory McIlroy as World Number One with victory.
"I can't speak for tomorrow given it's the last round and if I have a chance coming down the stretch, if it creeps in, I'll embrace it. I'll embrace the opportunity that presents itself.
"I don't look at it as a negative thing, I look at it almost as an advantage. Why should it add more pressure in a negative way? If it adds more pressure, it just makes me feel like this is something that's a little more special, let's go ahead and get the job done.
"I know it's easier said than done, but when you say added pressure, most people associate that with negativity or something that can hinder what's comfortable. For me, I think it could be advantageous. You hit the ball a little bit further, you can really get your mind around a more specific target and block out other things."
American Dustin Johnson, who three-putted the 72nd hole in the US Open last month to finish a shot behind Spieth, found his overnight lead intact when he teed off at 3pm, but struggled to a third round of 75.
