Fellow Americans Jimmy Walker and Nick Watney finished joint fourth on 279, while Australia's Aaron Baddeley was in a group tied for sixth another shot back.
"As soon as Michael expressed interest, Vince went from being a small role to being a major part of the show, " said "Vegas" executive producer Greg Walker, who created the series with Nick Pileggi.
The Clarets, founder members of the Football League, played with freedom and ambition - and should have doubled their lead after the break but Nick Montgomery blocked Joey Gudjonsson's hooked shot while Kyle Walker made a superb challenge with Robbie Blake poised to strike.