Williams tied the game at 10-10 less than five minutes into the game, then added back-to-back field goals and a three-point play to spark a 16-2 run that gave the Mean Green the lead for good, 24-12 midway through the first half.
Chad Frazier drilled a 3-pointer with 16:13 left to bring the Blazers back and cut the lead to a point, 46-45, but Williams fed Maurice Aniefiok and T.J. Taylor for 3-pointers that pushed North Texas to a 55-48 lead.
North Texas (11-8, 2-3 Conference USA) overcame a 53-39 rebounding deficit by shooting 49.2 percent from the field (29 for 59). Jordan Williams added 16 points for the Mean Green.
Frazier led UAB (12-6, 1-3) with 20 points.