Butler was 16 of 34 for 194 yards. Smith had seven catches for 109 yards and Telvin Hooks had 117 yards on the ground.
Florida A&M scored first on an 83-yard punt return by DeVondrick Nealy. Tennessee State (3-1) responded with Ronald Butler's 12-yard touchdown pass to Mahlon Medley with 17 second to go before halftime.
The Rattlers (0-4) took a 14-7 lead with a 46-yard touchdown pass from Carson Royal to Kareem Smith early in the third, but the Tigers ran off the next 23 points.
Smith hauled in a 38-yard score, and Colby Blanton's punt pinned A&M on their own 1, resulting in a safety. Smith caught another touchdown pass - this one for 32 yards - and Erick Evans' 1-yard plunge capped the scoring with 31 seconds to go.
AP College Football website: www.collegefootball.ap.org