McCarron finished 20-of-26 passing with one interception. Drake ran for a touchdown and blocked a punt as the Crimson Tide (3-0) overcame a sluggish start with 14 fourth-quarter points
Clinging to a 17-6 lead late in the game, Alabama finally broke it open when McCarron hooked up with DeAndrew White on a 30-yard TD pass.
The Rams (1-3) fell in the return of Coach Jim McElwain to Tuscaloosa, where he was offensive coordinator from 2008-11.
Garrett Grayson completed 24-of-38 passes for 228 yards for Colorado State.