The Crimson Tide (1-0) got one touchdown pass apiece from Greg McElroy and A.J. McCarron and overcame the loss of Heisman Trophy-winning running back Mark Ingram, who was shelved after having surgery on his left knee this week.
Also missing for Alabama was defensive end Marcell Dareus. He was ruled ineligible for two games due to dealings with sports agents.
Alabama piled up nearly 600 yards of total offense in the lopsided win.
The Spartans (0-1) got their only score on Harrison Waid's first-quarter field goal.