The Bearkats (1-1) jumped out to a 28-point lead in the first half as Johnson had touchdown passes of 9 yards to Rickey Smith and 48 yards to Jeff Thomas.
Alabama State (0-1) cut into the lead in the third quarter when Daniel Duhart and DeMario Bell connected on a 69-yard score to make it 38-17. Sam Houston State answered with a 68-yard touchdown from Johnson to Hill.
Hill finished with 123 yards receiving and added another 63 rushing. He fumbled into the end zone on the Bearkats' opening drive, but Zachary Stevens recovered it for a score. Donavan Williams had 12 rushes for 83 yards and a touchdown.
Duhart was 17 of 32 with 259 yards, two touchdowns and an interception for the Hornets.