The 34-year-old carded a three-under-par 67 to end on five under alongside American Ricky Fowler at Avenel Farm.
Kyle Stanley, 29, beat fellow American Charles Howell III on the first hole of a play-off after both shot a final-round 66 to end on seven under.
They also secured places at The Open at Royal Birkdale from 20-23 July.
"Anytime you can play in an Open, that's my favourite tournament of the year," said Laird.
"To have the chance to play it anytime is special. I've heard great things about Birkdale."
Four Open qualifying spots were on offer for the leading four players in the top 12 in Maryland who were not exempt.
South Korean Sung Kang, who finished in an eight-way tie for fifth, also qualified.
Stanley holed a putt after Howell missed from 10 feet to claim his first on the PGA Tour in more than five years.
"I'm thrilled," Stanley said. "It's a special week. I knew it was just a matter of time."
Scotland's Martin Laird qualified for this month's Open Championship by finishing tied for third at the Quicken Loans National in Maryland.