Mullen, a team mate in Britain and Ireland's Walker Cup victory last month, hit eight birdies and an eagle two in his identical score, also at Kingsbarns, on the Scottish east coast.
They share the lead with Sweden's Kristoffer Broberg, who made his 64 at St Andrews.
"What I did as an amateur worked, so I didn't see any reason to change it," Englishman Mullen told reporters after his maiden professional round.
Dunne's highlight was his 205-yard effort at the 15th, which gained him three shots. The Irishman also recorded eight birdies in his round at Kingsbarns.
"I kind of needed it," he said. "I got off to a bit of a ropey start. I was hitting a lot of poor full shots."
Of his hole in one, he said: "It was exactly as I pictured it ... I thought I hit it close and when I saw it drop, it was great. Nice little bonus there."
Broberg had taken an early lead on day one, with a 64 that also featured eight birdies but no bogeys.
Denmark's Soren Kjeldsen and English pair Richard Bland and Anthony Wall are a shot further back.
But defending champion Oliver Wilson is way off the pace after the first day, shooting a two-over-par 74 at St Andrews.
(Reporting by Neville Dalton)
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