Estill was seven of 11 and Bogans shot six of 11. Kentucky (3-1), won its third in a row after a surprising season-opening defeat at home to Western Kentucky.
Tayshaun Prince added 17 points for the Wildcats, who were facing the Golden Flashes for the first time and playing their first contest away from home.
Antonio Gates led Kent State with 22 points. Trevor Huffman added 18 and Demetric Shaw 16 for the Golden Flashes (3-2), who had a three-game winning streak snapped.
In a back-and-forth first half, Bogans scored 11 points and Eskill added eight to give Kentucky a 37-35 lead after 20 minutes. Gates led Kent State with 13 at the break.
The Golden Flashes took a 32-31 lead on a pair of free throws by Anthony Wilkins, but Kentucky quickly regained the lead on a layup by freshman Chuck Hayes and did not trail again.