After trading the lead back-and-forth midway through the second half, UAB led by six with 3:20 left. Matt Bingaya made it a four-point game with a jumper and Rasham Suarez brought Southern Miss within three with a free throw with 1:22 remaining.
Brown drilled a jumper next time down for UAB, and then Nick Horton and Watts made free throws to provide the final margin.
Chris Cokley added 11 points and seven boards for UAB.
Bingaya led Southern Miss (5-11, 0-5) with 17. Suarez finished with 16 points and Norville Carey added 14.