Taylor Murray led Kentucky (12-13, 4-7) with 23 points and Maci Morris had 22.
The Wildcats, down 59-46 after three quarters, made 11 of 17 shots in the fourth quarter, including 4 of 6 3s, to put the pressure on. Missouri made 15 of 18 free throws in the fourth quarter, 12 of the makes coming in the final 2½ minutes.
A 3-pointer by Murray with 7.1 seconds left made it a 3-point game, but Cunningham iced it from the line with 6.8 seconds left.
Missouri finished 10 of 21 from distance with Cunningham 5 of 7 and Smith 3 of 6.