DeJeon Jarreau led the Cougars with 16 points. Quentin Grimes added 13 points and Justin Gorham 10.
Ricky Council added 11 points for Wichita State, which had its first home victory against a top-six opponent since beating No. 2 Louisville on Feb. 25, 1967. The Shockers also snapped a six-game losing streak against Houston.
Houston led by as many as 12 points in the first half before Wichita State stormed back and cut the deficit to 34-33 by halftime.
Gilbert hit consecutive 3-pointers to cap an 11-0 run by Wichita State at the start of the second half.