A Ben Smith layup, assisted by Murry, pushed the Shockers ahead 23-22 with about five minutes remaining in the first half.
The Sycamores held a 29-25 lead in the final minute of the opening period. Two Stutz free throws cut the Sycamores' lead to two points before an Odum three-pointer at the buzzer pushed Indiana State ahead 32-27 at the half.
Murry led the Shockers with eight first-half points. Carl Hall added seven for Wichita State. Stutz picked up three blocks. Odum put up nine points for the Sycamores. Indiana State's Jordan Printy and Walker led all players with five rebounds each.
The Shockers shot just 24.1 percent (7-of-29) in the first half and went 0-for-7 from the three-point arc.
Wichita State's shooting turned around in the second half as the Shockers made 16-of-27 shots (59.3 percent).
A Stutz dunk, assisted by Joe Ragland, cut the score to 36-33 early in the second half. Stutz's free throws soon after cut the Sycamores' lead to one point.
A Murry jumper gave the Shockers a 37-36 lead with about 15 minutes remaining and a hook shot gave the Shockers a 39-36 edge and ignited the crowd.
A Smith tip-in pushed the Shockers' lead to five points at the 13:47 mark and extended the Shockers to a 10-0 run over 3:50.
Two Hall free throws, followed by Stutz and Hall layups, gave the Shockers an 8-0 run midway through the half.
Indiana State crept to within three points before a Stutz layup gave the Shockers a 60-55 edge. A steal and layup from Murry pushed Wichita State ahead by seven with 3:36 on the clock.
Wichita State's lone three-pointer of the game, made by Smith, extended the Shockers to a nine-point edge - their largest lead of the game with 2:02 remaining.
The Sycamores got as close as four points in the closing seconds, but Stutz made six free throws in the final minute to help seal the win.
Wichita State has now won 10 of its last 11 games. The team's lone loss during the stretch came in triple overtime on the road at Drake.
The Shockers also improved to 12-1 at home this season and secured their third-straight 20-win season with Saturday's victory.