Goodwin finished just shy of a triple-double for the Wildcats (4-1) after adding nine rebounds and nine assists, while fellow freshman sensation Poythress went 9-of-12 from the field to help Kentucky extend its home winning streak to 55 consecutive games, the longest active stretch in the nation.
Nerlens Noel made 9-of-11 attempts in an 18-point night, with Julius Mays contributed 15 points in the rout.
The Wildcats shot a scorching 66.7 percent as a team, their highest mark in head coach John Calipari's four seasons.
Julian Boyd and Jamal Olasewere each had 22 points for the Blackbirds (0-4), who opened up a six-point lead just past the midway point of the first half before faltering.