Fred VanVleet had 16 points and nine assists for the Shockers (9-5, 3-0 Missouri Valley Conference), who have won four straight.
Trailing 32-27 at halftime, Evansville rallied to tie it at 57 with 3:32 left after Jaylon Brown's layup. Evan Wessel hit a go-ahead 3-pointer, Grady made a layup, and the Shockers were back on top 62-59 with 2:11 to go.
Zach Brown's 3-pointer made it a two-possession game, 67-62, with 19 seconds left, but Evansville's Mislav Brzoja missed a 3 and two free throws from Egidijus Mockevicius were not enough.
Wichita State scored 13 points off of 13 Evansville turnovers and outscored the Purple Aces 24-20 in the paint.
Brown scored 18 points, D.J. Balentine added 14, Adam Wing had 12 and Mockevicius grabbed 15 boards for Evansville (13-3, 2-1).