Butler was 12 of 27 for the Tigers (4-1). Telvin Hooks ran for 54 yards and a touchdown on 10 carries.
Terrell Bonds scored for Tennessee State on a 43-yard interception return midway through the second quarter. Clark kicked his second field goal in the last few seconds of the first half and the Tigers led 20-0 at the break.
The final Tigers score came in the fourth quarter when Samquan Evans recovered a fumble by the Rattlers' backup QB Carson Royal following a sack and took it in for the score.
The Rattlers (0-4) did not score until early in the third quarter on a 16-yard run by Damien Flemming. Flemming finished with 15-of-30 passing for 113 yards and threw two interceptions.