Two free throws by Xavier Richards gave Tennessee State a 34-28 lead with 17 minutes to play, but a jumper by Smith started a 28-5 run, which was capped by a Bradshaw 3-pointer and gave the Bruins a 17-point lead with 9:03 left.
The Tigers then trailed by double digits until the final minute.
Tennessee State (3-18, 0-6) used a 16-4 run to open up a 25-10 lead with nine minutes left in the first half. Belmont responded with an 18-5 spurt and trailed 30-28 at the break.
Tennessee State has lost six in a row and 17 of its last 18 games.