Koepka and Stroud tied for second, two shots behind winner Thorbjorn Olesen, while Cink finished tied for ninth.
The 25-year-old Koepka began his professional career on the European Challenge Tour, winning four times on the development circuit before picking up his first European Tour victory last November at the Turkish Airlines Open. The winner at the PGA Tour's Waste Management Phoenix Open in February, Koepka was recently passed over as a pick for the U.S. Presidents Cup team, with captain Jay Haas' selections going to Bill Haas and Phil Mickelson. Following Jim Furyk's announcement that he'd be unable to compete in South Korea because of a wrist injury, Haas chose J.B. Holmes, who was next in Presidents Cup points, as his replacement.
Koepka authored a final-round 67 on the Old Course at St. Andrews and trailed by just one on the back nine before losing steam down the stretch and making par on his final four holes. He is currently ranked 13th in the Race to Dubai standings.
Stroud, the 33-year-old who remains in search of his first professional win, made seven birdies against three bogeys to shoot 4-under 68 and tie Koepka for runner-up.
Cink, meanwhile, the 42-year-old former Open champion, got off to a blistering start, making six birdies on his first 10 holes before playing the rest of his round 2 over to close with a 68 of his own. His only other worldwide top 10 this year came in the form of a T-5 at the RBC Canadian Open.
No American has won the Alfred Dunhill Links since its inception in 2001.