Jeremiah McGeough punted the ball into his own player on Delaware State's opening possession and Leroy Holt recovered it in the end zone to give Bethune-Cookman (4-1, 1-0 Mid-Eastern Athletic Conference) a 7-0 lead less than 2 minutes in.
Quentin Williams extended the lead with touchdown passes to Jhomo Gordon and Jones before Delaware State (1-5, 1-1) cut the deficit to 21-7 on Terrick Colston's 11-yard interception return with 5 seconds left in the first quarter.
Neither team scored again until Anthony Jordan's 1-yard touchdown run early in the fourth quarter. Jordan finished with 12 carries for 62 yards.
Williams was 20 of 26 for 198 yards, two touchdowns and an interception.
Delaware State was 0 for 14 on third-down conversions and managed just 168 yards of offense.