Kentucky went ahead 8-6 on a layup by Ryan Harrow and never trailed again.
Leading 10-9, Kentucky went on a 13-0 run for a 23-9 lead.
UK went into halftime with a 42-34 lead. UK is 17-1 this season when ahead at intermission. Cauley-Stein had 12 points in the first half, just two away from his career high. Goodwin also had 12, his first double-figure outing in four games.
Kentucky stretched the lead to 58-45 with 9:03 to play before VU went on a 10-0 run to slice the margin to 58-55.
Poythress responded with a dunk and free throw to make it 61-55 but VU got a couple of buckets from Josh Henderson to make it 61-59.
At that point, Julius Mays made a series of big plays, helping account for eight of UK's last 13 points.
He blunted the momentum with a three at the 3:23 mark, his second longball this half with the shot clock near expiration, to make it 64-59.
On the next possession, he tossed a lob for a Cauley-Stein dunk to make it 66-60.
He made three of four foul shots in the final minute.
As a team, UK made six of eight foul shots in the last minute of the game to keep VU at bay.
Kentucky shot 51.8 percent from the field and the Wildcats are 9-0 this season when making at least half their shots.
UK won points in the paint 38-24.
Willie Cauley-Stein scored a career-high 20 points, adding seven rebounds and three blocked shots.
Tied his previous career best (14) on the first possession of the second half.
Made his first six field-goal attempts and finished 8 of 10 from the field.
He has eight double-figure scoring games this season, including four of the last five.
First Wildcat to reach 20 points since Goodwin and Wiltjer each did so at Ole Miss.