Harrison netted 21 points and Young put in 20 for the Wildcats (16-5, 6-2 SEC), who got back on the winning track following Tuesday's loss to Louisiana State.
Julius Randle contributed 18 points and nine rebounds.
The Tigers (16-5, 4-4) got a career-high 33 points from Jabari Brown. Jordan Clarkson scored 28 for Missouri.
Celebrity Breakups and divorces of 2014 [PHOTOS]