The Wildcats (15-4, 5-2 Southeastern Conference) led throughout thanks to strong shooting, finishing at 55 percent from the field. Ulis' scoring was balanced, with 11 of his points coming during a second half in which Kentucky led by as many as 21. He finished 9 of 13 from the field with two 3-pointers.
Murray meanwhile was 7 of 13 from the field including 3 of 6 from long range. Alex Poythress got Kentucky started in both halves for 16 points on 8-of-10 shooting with many coming inside.
Kentucky held Vanderbilt (11-8, 3-4 SEC) to 32 percent shooting and 33 percent from behind the arc to halt the Commodores' three-game winning streak.
Kentucky controlled the paint 34-18 while finishing even with Vanderbilt on the boards 32-32. The Wildcats rolled despite shooting just six free throws, making four. The Commodores were 20 of 25 and none of it mattered.
The Wildcats' second straight SEC win came a week after a loss at Auburn that left them soul searching after blowing a double-digit lead. They've answered with two straight wins and met another challenge against a Commodores squad that appeared headed in the right direction after starting 0-3 in league play.
Vanderbilt had sought a statement win to go along with its resurgence and presented multiple threats, from the 7-foot duo Luke Kornet and Damian Jones to a potent perimeter shooting 41 percent from long range.
Neither were factors in a shooting performance almost as cold as outside temperatures in the mid-20s at tipoff.
Poythress seemed determined to do his part inside early despite giving away several inches, muscling inside for layups along with a layup.
Poythress and Ulis combined for 18 first-half points while Murray warmed up to add nine and help spur Kentucky's 37-27 halftime lead. More impressive was the Wildcats' defense that forced eight turnovers leading to 13 points and limited Vanderbilt to just four points in the paint through 20 minutes.
Poythress wasn't done, scoring six straight points to ignite Kentucky's 18-13 run coming out of the break for a 55-40 lead that wasn't threatened. The Wildcats steadily stretched it to 67-46 with 8 minutes remaining en route to their 31st straight win at Rupp Arena, where Vanderbilt hasn't won since 2007.
Vanderbilt: The Commodores arrived two days early to get ahead of a snowstorm that dumped a foot of snow in the city but fell to 7-62 all-time in Lexington.
Kentucky: Derek Willis was quiet offensively with seven points but led the Wildcats with nine rebounds.
Vanderbilt hosts Florida on Tuesday.
Kentucky hosts Missouri on Wednesday.