The Jayhawks (30-5), flummoxed by the Hilltoppers' full-court pressure, trailed 31-30 at halftime. Kansas eventually built an 11-point lead in the second half, but couldn't put Western Kentucky away until Ben McLemore's two foul shots with 11 seconds left in the game.
McLemore and Travis Releford scored 11 each for the Jayhawks (30-5), who wearily advanced to play No. 8 seed North Carolina and former coach Roy Williams in the South Regional on Sunday.
Jamal Crook scored 13 points and T.J. Price had 12 for the Hilltoppers (20-16), who would have made history by becoming the first No. 16 seed to upend a No. 1 seed in the tournament.
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