Rice was playing the game on its home turf, in the second annual Bluebonnet Bowl.
Ken Coleman of Wichita ran for a 1 yard touchdown for Kansas, but the extra point fell short.
Johnny Burrell caught a 5-yard touchdown pass from Randy Kerbow to give Rice a 7-6 lead.
When Kansas was forced to punt later in the quarter, John Hadl mishandled the snap and ran 41 yards to give the Jayhawks crucial position.
Coleman would score his second touchdown of the day to give Kansas a 12-7 lead at halftime.