The Wildcats (5-1) led by 15 points midway through the second half and appeared to have the game in control but eventually saw their lead cut to 56-54 with 5:03 remaining after a pick-and-roll layup by George Washington’s Arnaldo Toro.
Kansas State closed the game on an 11-5 run, using its man-to-man defense and clutch free-throw shooting, to secure the win.
Dean Wade added 17 points, and Barry Brown Jr. chipped in 15 for Kansas State, which led 38-29 at halftime. The Wildcats shot 46.9 percent from the field, and finished 16 of 18 from the line.
George Washington (2-4) outrebounded Kansas State 37-26 but shot just 38.5 percent in the second half.
Toro had 21 points and nine rebounds to pace George Washington. Patrick Steeves had 11 points, and Jair Bolden scored nine for the Colonials.