Reserve center Shagari Alleyne had 11 points, eight rebounds and six blocked shots for Kentucky.
Morehead State (4-2) trailed only 29-23 at halftime, but the Eagles didn't get their first second-half basket until 11:07 remained. Morehead State _ coached by Kyle Macy, a member of Kentucky's 1978 NCAA championship team _ shot 27.3 percent from the field and committed 24 turnovers.
Morehead State had the fewest points by a Kentucky opponent since South Carolina lost 74-40 to the Wildcats in February 1999. It was the fewest points scored in a game by Morehead State since the 1948-49 season, when the Eagles had 31 in a loss to Eastern Kentucky.
During Kentucky's 20-0 run, Azubuike scored nine points and Patrick Sparks had eight _ including two 3-pointers _ and an assist on a dunk by Randolph Morris. Sparks finished with 10 points and six assists.
The run put Kentucky up 49-23 with 14:54 left. Morehead State came no closer than 21 points the rest of the way, and the Wildcats extended the lead to as many as 35 points.
Kentucky was just 3-of-18 from 3-point range and shot 39.4 percent from the field.
Kentucky took leads of 8-0 and 24-8 as Morehead State made only three of its first 17 field goal attempts. The Eagles didn't reach double digits on the scoreboard until almost 12 minutes into the game.
But Kentucky went scoreless for more than 6 minutes, allowing the Eagles back in the game. A 12-0 run cut the Kentucky lead to four, and the Eagles came as close as 26-23 before Kentucky took the 29-23 halftime lead.
Kentucky is 8-0 all-time against Morehead State. The schools are located about 65 miles apart.