Bradford had the highest completion percentage for a rookie in NFL history two years ago but struggled in 2011 after an early season ankle injury that cost him six games.
While most teams rest their key starters during the final preseason contest, Bradford saw plenty of action while completing 11-of-16 passes for 175 yards.
He accounted for the first three St. Louis scores, which came on throws of 14 yards to Austin Pettis, 7 yards to Danny Amendola and 9 yards to Michael Hoomanawanui.
Janoris Jenkins then tacked on a 76-yard interception return of a pass by Curtis Painter to put the Rams in front 28-0.
It was one of three interceptions by Painter, who also threw for two touchdowns.
Both teams split their four exhibition games. St. Louis will begin its season in Detroit and Baltimore will host Cincinnati.