Javeres Brent scored 11 points, including three 3-pointers, and Derrell Taylor scored 10.
Jackson State (1-2) was outshot 43.1 percent from the field (22 of 51) to 45.2 percent (19 of 42) for Jacksonville. The Tigers got good penetration on offense, scoring 30 points in the paint to 10 for the Dolphins, and scored 19 free throws to the Dolphins' 10 on 23 tries.
The teams traded baskets and played to a 27-27 first-half tie, with the Tigers hitting 10 free throws.
Jackson State used a 14-3 second-half run capped by a layup by Bernard to lead 43-35 at 13:38. Dre'Sean Looney finished with six straight free throws.