With a closing 4-under 66, Kirk got to 12-under 268, one ahead of Masters champion Jordan Spieth, playing partner Brandt Snedeker and Jason Bohn.
After Kirk hooked his tee shot at No. 18 into the left rough, he hit his approach from 155 yards over the green. A nice chip set up the winning putt.
Snedeker, who closed with a 67, hit a similar tee shot as Kirk on the final hole and hit to 12 feet. But his birdie try that would have tied Kirk slid left of the hole.
Bohn had a 63 that included six consecutive birdies on the front nine. Spieth shot 65, with a near-birdie that became a bogey at the par-3 16th hole.