Freshman Perry Ellis added 12 points and Ben McLemore chipped in with 11 for the Jayhawks (3-1), who will meet Saint Louis in Tuesday's championship game at the Sprint Center.
Kevin Young hauled down nine rebounds for Kansas, which shot 47.2 percent from the field in the victory.
Brock Motum led the Cougars (2-2) with 14 points and seven boards.
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