He carded a 66 to finish at 14-under-par 266, while fellow American Baird (67) and South African Tim Clark (62) tied for second on 13-under at the Seaside Course on Sea Island.
Kirk, 28, collects $990,000 and an invitation to next year's Masters.
"It's unbelievable to be here at Sea Island, at my home," he told Golf Channel.
(Reporting by Andrew Both in Tokyo, editing by Gene Cherry)
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