The Wildcats (13-4, 3-1 Southeastern Conference) made 23 of 24 from the line including their first 17 before Aaron Harrison, Andrew's twin, missed the front end of a 1-and-1 with 32 seconds remaining.
The Wildcats had entered the game making 66 percent of their free throws, 63 percent in SEC games.
Andrew Harrison made all 10 of his free throw attempts along with a couple of 3-pointers and freshman Julius Randle was 5 of 5 from the free throw line and 6 of 9 from the field for 18 points.
Kentucky overcame a nine-point first-half deficit to beat the Volunteers (11-6, 2-2) in this season's lone scheduled meeting between the schools. Trailing 18-9 with 12:16 left in the half, the Wildcats closed with a 25-14 run over the final 11:06 and led by as many as 11 points in the second half.
Kentucky was outrebounded 39-24 by the Vols, who made just 16 of 23 from the free throw line.
Aaron Harrison finished with 14 points including two from beyond the arc to help the Wildcats finish 7 of 16 from 3-point range. He was 6 of 7 from the free throw line.
Jarnell Stokes had 20 points and 15 rebounds for Tennessee, which lost to Kentucky for the 150th time in the series that dates to 1910.
Tennessee shot well from the field and the free throw line in Wednesday night's victory over Auburn. The Volunteers committed just 12 turnovers after coming in last in the SEC with a minus-7.5 margin in league play, but that was still four fewer than Kentucky.
The Wildcats succeeded in making Tuesday night's heartbreaking 87-85 overtime loss at Arkansas a distant memory. While the Wildcats insisted there were no lingering mental effects from Michael Qualls' last-second rebound dunk that snatched away another winnable game, they also stressed the need not to let it happen again.
Payback was also on Kentucky players' minds after last year's 30-point loss in Knoxville just days after Nerlens Noel's season-ending knee injury. It was Tennessee's most lopsided win in the series and the Wildcats were determined to make amends.
Kentucky's quest appeared difficult early as Stokes seemed primed to beat the Wildcats by himself. He scored the game's first six points en route to a 12-point, 11-rebound first half that symbolized the Vols' energetic effort: they outrebounded the Wildcats 23-10 in the first 20 minutes and built a lead that stood for most of the half.
And yet, Stokes' performance and Tennessee's statistical edge mattered little at halftime as Kentucky emerged with a 34-32 lead thanks to its run that included a 16-6 spurt over the final 7:06. James Young's 3-pointer with 54 seconds remaining capped the surge, but 26 combined points by Randle and Andrew Harrison carried the Wildcats.
Randle scored 16 points in the first half and got things going by scoring Kentucky's first five points including his first 3-pointer this season after seven misses.
The second half belonged to the Wildcats, who shot 46 percent from the field and finished 22 of 50 overall (44 percent). Tennessee finished 24 of 58 (41 percent).