The Pirates (3-1) recovered from a tournament-opening loss to Long Beach State by holding off the Braves (2-3) down the stretch.
Seton Hall closes the eight-team tournament by facing Mississippi in the fifth-place game Sunday. Bradley takes on Towson in the seventh-place game, the loser getting shut out in Charleston.
The Pirates guaranteed they wouldn't face that by opening a double-digit lead early that Bradley could not overcome. Veer Singh hit two 3-pointers and Rodriguez had 6 straight points to put Seton Hall ahead 25-15.
Bradley closed to 56-52 in the final six minutes on a driving layup by Dwayne Lautier-Ogunleye. However, Rodriguez and Carrington hit consecutive baskets to build the lead back.
Lautier-Ogunleye finished with 19 points for Bradley.