Taylor, who scored nine of his 24 points in overtime, drained the clutch foul shots after Missouri's Michael Dixon had given the Tigers a one-point lead on a basket with 12 seconds remaining.
Kansas (24-5, 14-2 Big 12) clinched at least a tie for the Big 12 Conference title with the win.
The Jayhawks battled back from a 19-point second-half deficit and remained undefeated at home with the help of Thomas Robinson, who notched 28 points and 12 rebounds.
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