A last-second 3-pointer by T.J. Price pulled the Hilltoppers within 30-28 at halftime. He tried the first shot of the second period -- another 3-pointer -- but missed and Cleanthony Early fed Ron Baker for a 3-point shot that started a Wichita State (2-0) spurt.
Coleby scored the game's next six points, with four coming on dunks, and Baker set up a Tekele Cotton jump shot that completed an 11-0 run and put the Shockers ahead 41-28 4 minutes into the second half.
Western Kentucky (0-1) cut the deficit to single digits just once after that and then for only 11 seconds before Cotton dropped in two shots and Fred VanVleet made two free throws that made the Shockers' lead 15 points.
VanVleet finished with a game high 17 points while Coleby had 13, Early 11 and Cotton 10 points Wichita State. Western Kentucky, which shot just 28.6 percent from the floor, got 12 points each from Aleksej Rostov and Price.