Stallings held a four-stroke lead when third-round play was suspended Saturday night, but he picked up where he left off Sunday morning, completing Round 3 with an 8-under-par 64 and then firing a 4-under 68 during the final round.
He never surrendered the lead throughout the day, finishing at 24-under 264 thanks to a pair of birdies late in his final round en route to his second career PGA Tour win.
That was two shots better than Jason Bohn, who registered a 3-under 67.
The heavy Sunday workload was necessitated by more than 10 hours of rain delays over the Mississippi tournament's first three days.
Billy Horschel, who had pulled to within one stroke of Stallings at one point, managed a 1-under 71 and ended up alone in third at 20-under 268.