Makol Mawien added 15 points for Kansas State (10-2), which has won six of its past seven games.
Carter Skaggs had 24 points and Malachi Flynn 23 for Washington State (7-4), which overcame a dreadful first half to take the lead in the second half.
Neither team shot well. Kansas State finished at 42 percent shooting while Washington State shot 38 percent.
Mawien scored eight points as Kansas State jumped to a 21-9 lead.
The Wildcats led 35-25 at halftime, after holding Washington State to 29-percent shooting (9-of-31). Kansas State wasn’t much better, shooting 39 percent in the first.
Skaggs had 13 first half points for Washington State.
Washington State found its shooting range in the second half.
Skaggs hit a pair of 3-pointers as Washington State opened the second half with an 11-4 run to cut its deficit to 39-36.
Flynn’s layup and free throw gave Washington State its first lead at 49-47 with 10 minutes left. Flynn sank a pair of 3-pointers to give the Cougars a 57-49 lead.
Brown made six straight points as Kansas State came back and trailed 63-62 with 1:26 left.
Brown’s dunk put the Wildcats ahead 64-63 with 51 seconds left.
Flynn missed a long jumper and Kansas State rebounded. Brown hit a pair of free throws and the Cougars missed another long jumper.