The Blazers (5-3) trailed by four, 29-27 in the final minute of the first half. Williams knocked down a 3-pointer with 36 seconds left to cut the deficit to a point.
Cokley hit the first four field goals as UAB traded baskets to start the second half. William Lee put the Blazers in front for good with a 3-point play with 12:52 left in the game to start a 19-2 run.
UAB finished shooting 50 percent from the field (28 of 56), including 9 of 22 (40.9 percent) from beyond the arc.
DeVaughn Akoon-Purcell scored 18 points and made 8 of 20 shots from deep to lead Illinois State (3-5).