Bradford needed to complete only 12-of-16 passes en route to the trio of touchdown tosses, compiling 117 yards as the Rams (3-3) notched a second straight victory.
Lance Kendricks, Brian Quick and Cory Harkey each hauled in a scoring strike and rookie Zac Stacy picked up 79 yards on the ground for St. Louis.
Matt Schaub left in the third quarter with a right ankle injury after making good on 15-of-21 passes for 186 yards for the struggling Texans (2-4), who dropped their fourth straight.
Arian Foster rambled for 141 yards on 20 carries and reeled in four passes for 57 yards in the loss.
Celebrity Families of 2014 [PHOTOS]