Devante Wallace and Lorenzo Cugini added 15 apiece for High Point (5-2). Brown hit 10 of his 12 free throw attempts as the Panthers made 84.8 percent (28 of 33) from the line compared to 9 of 15 for the Spartans.
Tevon Saddler made two free throws with 7:37 left to pull Greensboro within 54-51. But Wallace scored the next nine points - on four free throws, a layup and a 3-pointer - for a 63-51 lead.
The game was tied early at 21 until High Point closed out the final 5:25 of the first half with a 14-6 run, highlighted by two Cugini 3-pointers.