The Wildcats trailed by as many as 11 points late in the first half, but rallied to go in front 32-31 at the break. Morehead State led again by four in the second period before Kentucky finally took control.
Kentucky shot 51 percent from the field. The Wildcats went to the foul line 25 more times than did Morehead State and made 18 more. The Eagles were called for 31 fouls to just 11 for Kentucky.
Alex Polythress added 20 points for the Wildcats (3-1) and Nerlens Noel had 12 assists. Morehead State (3-2) was carried by Milton Chavis, who scored 23 points.
Kentucky has won all 10 meetings with its in-state rival.