Lee was playing his first game since Nov. 25, having missed nine contests with a broken collarbone. It was the 27th straight win for the Jayhawks over the Wildcats.
Kansas State (8-4, 0-1 Big 12) closed to within 67-63 lead on Marques Hayden's dunk with 1:55 left. But Wayne Simien, who paced the Jayhawks with 19 points, got a favorable bounce on a turnaround jumper that made it 69-63 with 1:38 to go.
Lee's free throws gave Kansas (10-2, 2-0) a 73-65 edge with 24 seconds remaining.
Keith Langford scored 17 points and Lee finished with 16 for the Jayhawks.