Brees connected on 18-of-26 passes, helping the Saints (9-0) increase their lead to four games atop the NFC South.
Bush also ran 3 yards for a score.
Roby opened the second half with his kickoff run.
Marc Bulger completed 26-of-40 passes for 298 yards and two touchdowns for the Rams (1-8)
Bulger, who was intercepted twice, hooked up with Donnie Avery on 29 and 19 yard scoring passes.
Steven Jackson ran for 131 yards, including a 2-yard touchdown, for St. Louis.
Notable deaths of 2014 [PHOTOS]