The Blazers (11-11, 7-2 Conference USA) shot 16 of 21 free throws and outrebounded the Roadrunners 43-29, including 17-9 offensive boards.
San Antonio led 20-11 after a jumper by Ryan Bowie, but UAB used a 12-2 run in which Watts scored six to pull ahead 25-24. The Roadrunners retook the lead on free throws by Keon Lewis, but Watts hit a 3-pointer to put the Blazers up 33-29 at halftime.
UAB pulled ahead on a 7-2 second-half run, then led 53-41 after a 3 by William Lee. UTSA gained ground on a 10-2 run, closing within 60-55 after Jeromie Hill hit back-to-back 3s, but UAB made five free throws in the final 49 seconds to hold on.
Hill led the Roadrunners (10-10, 4-5) with 20 and Kaj-Bjorn Sherman added 13.