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).
Putin thinks Obama would save him if he were drowning
Justin Bieber crashes Drake Bell's album release party