Winthrop's Keon Johnson missed the front end of a one-and-one and Brown was fouled going for the rebound. Brown's free throws sent the Panthers (18-7, 9-4) into a four-way tie for first in the Big South.
The Panthers closed to within one, 72-71, with 5.1 seconds remaining on two free throws by Devante Wallace.
High Point had trailed for the final 8 1/2 minutes after Keon Moore made two free throws and the Eagles built a 10-point lead, 70-60, on Moore's 3-pointer with 3:28 remaining. Brown and Wallace combined on a 9-2 run to set up the final sequence.
Moore led Winthrop (13-11, 8-5), which lost at High Point for the seventh straight time, with 25 points, hitting seven 3-pointers.