Laird shot a 68, McNeill 67 and Campbell 69 in the final round.
The win was the first on the PGA Tour for Laird, a native of Glasgow, Scotland. He collected a first-place check of $756,000.
"I was amazed how calm I was coming down the stretch," Laird said.
Jim Furyk fired a 10-under 62 to finish at 266, sharing fourth place with Jeff Klauk (68) and Charley Hoffman (68).
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