Laird, who has been based in the United States for the last decade, is searching for his second win on the PGA Tour following his breakthrough victory at the 2009 Las Vegas Open.
An eagle at the par-five 16th, the Scot's seventh hole of the day, made the difference for the 28-year-old who sank a 30-foot putt there after hitting his second shot from the rough.
The Scotsman has quietly risen up the world rankings to 40th but has enjoyed an excellent March, tying for 10th in the WGC-Cadillac Championship at Doral before finishing joint fifth at last week's Transitions Championship in Tampa.
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