The Wildcats (30-0, 17-0 Southeastern Conference) had won their previous five games by an average of 24 points.
They were really challenged in this one by Georgia (19-10, 10-7), which had the sellout crowd roaring when Yante Maten tipped in a miss of his own shot to put the Bulldogs up 56-47 with 9 minutes remaining.
But Kentucky showed it knows how to win the close games, too. The Wildcats began pounding the ball inside to 6-foot-11 freshman Karl-Anthony Towns, who managed to stay in the game until the closing seconds after picking up his fourth foul.
Kentucky seized the game with a 14-0 run, and Georgia hurt its chances by missing three straight 1-and-1.
Towns led the Wildcats with 19 points.
Nemanja Djurisic topped Georgia with 18 points.