The Wildcats led 49-35 at the half.
After Austin Peay closed to 40-31 on Anthony Campbell's dunk with 3:54 left, Kentucky ended the half with a 7-0 run and was not challenged in the second stanza.
DeMarcus Cousins scored 19 points with eight rebounds, John Wall had 17 points, six assists and four rebounds and Darius Miller added 11 points for the Wildcats (11-0), who held a 40-23 rebounding advantage and shot 50.8 percent from the field.
Wes Channels led Austin Peay with 21 points and five rebounds.
Duran Roberson scored 16 with four rebounds, and John Fraley scored 13 with three rebounds for the Governors (7-5), who had won four in a row.
They lost despite committing only 11 turnovers to 16 by the Wildcats.
Celebrity Families of 2014 [PHOTOS]