Doron Lamb led the Wildcats (2-0) with 17 points and Terrance Jones chipped in 15 points.
Tyshawn Taylor led Kansas (1-1) with 22 points. Thomas Robinson contributed a double-double of 11 points and a dozen rebounds to the cause.
The score was tied 28-28 at halftime as Kentucky struggled to get into a groove.
The Wildcats erupted for 47 points in the second half. Marquis Teague and Michael Kidd-Gilchrist both scored 12 points in the half for the Wildcats, who shot 52 percent from the field for the game compared to 33.9 percent for Kansas.