McNulty shared the lead with David Edwards when the round began but made birdie at the second and third holes to set a tone no one really challenged, despite his bogey at the fourth.
His 72-hole total was 16-under 272.
"It's my first major so it's like a fantastic accomplishment," McNulty said. “I was thinking about what David Toms did a few years ago at the Wachovia, and thought, no don't do something stupid like that."
He was referring to the bogey. Toms made a critical bogey late which cost him a shot at winning the Wachovia event in 2003.
Edwards (73) was second at 11-under 277. D.A. Weibring (72) was third at 10-under 278 and Keith Fergus (73) finished fourth at 9-under 279.
Swim Week Miami Beach 2014 [PHOTOS]