Shaw is still in search of its first win after a solid two-touchdown performance from quarterback Torrin Campbell. Marquis Gorham's only carry went for 39 yards and a touchdown.
The Bears led 21-12 with less than three minutes left. Bowie State blocked a punt and recovered it in the end zone for a touchdown to pull within two. David DuShon caught a 5-yard touchdown pass from Gaston Cooper with 18 seconds left for the final blow.
The Bears will play Chowan on the road next Saturday.