The Roadrunners (3-12, 1-1 Conference USA) had a 12-1 run to go up 73-52 with 8:06 to play but the Owls (5-10, 0-2) immediately responded with 13 straight to close within eight with 5:35 to play. The lead was 12 with three minutes to go when Marcus Evans had a 3-pointer and 3-point play back to back in a 10-0 run that cut it to 80-78 at 1:28.
However, two missed shots and Wilson's layup late in the shot clock followed by his two free throws sealed it.
Evans finished with 23 for Rice and Max Guercy had 11 points and six assists to surpass 1,000 points and 400 career helpers.
UTSA shot 56 percent to help offset 17 turnovers.