Stacy ran the ball 33 times, the most in his young career, and fellow rookie Stedman Bailey contributed a 27-yard touchdown run for the Rams (7-8).
Kellen Clemens paced the St. Louis offense, completing 16-of-20 passes for 158 yards.
The Buccaneers (4-11) fell despite five catches for 98 yards from Vincent Jackson.
Mike Glennon threw for 158 yards on 16-of-26 efficiency and Bobby Rainey ran for Tampa Bay's only touchdown.
Swim Week Miami Beach 2014 [PHOTOS]