The Bears (3-7) had a three-game home winning streak snapped.
Bulger had key third-down completions to Torry Holt and Isaac Bruce, and benefited from a pair of penalties on Chicago. Wilkins kicked his third field goal of the game and St. Louis (7-3) held on, even after Jerry Azumah returned the ensuing kickoff 38 yards.
Bulger completed 18-of-25 passes for 139 yards and two touchdowns in the second half, and Marshall Faulk carried 13 times for 82 yards after halftime for his first 100-yard game since Nov. 3, 2002. The Rams have won six of their last seven games.
Chris Chandler passed for 153 yards and a touchdown but was intercepted twice for Chicago, which fell to 3-2 at renovated Soldier Field.