Josh Williams made a jumper to cut Lipscomb's deficit to five with 4:25 remaining but Bradds made two free throws and then converted a 3-point play before Luke made a layup to put the Bruins up 82-70 less than a minute later.
Lipscomb (3-8) pulled within seven on a layup by J.C. Hampton with 2:31 to play, but would get no closer.
Belmont made 32 of 56 field goals (57 percent) and hit 21 of 24 free throws (88 percent).
Williams led the Bisons with 21 points.
The Bruins beat Lipscomb 105-89 on Dec. 1.