Chris Lofton, the Southeastern Conference's leading scorer, returned after missing four games with a sprained right ankle but was somewhat limited against the Tigers (13-10, 2-7).
The Volunteers (16-8, 4-5), trying to get in position for an NCAA tournament bid, helped themselves by staying undefeated at home this season at 12-0.
LSU tried to make it tough, but the Tigers lost a sixth straight game while leading scorer Glen Davis was held to a season-low five points.
The Tigers trailed the entire game and kept trimming the lead but it was never enough.
LSU got as close as 43-41 on Glen Davis' jumper with 15:31 remaining, and Tennessee rallied with a 13-2 run.
During the spurt the Vols went ahead 54-43 on consecutive 3-pointers by Lofton and Jordan Howell after Tennessee had missed seven in a row from long range. Ramar Smith's pair of free throws capped the run and put the Vols up by 13.
LSU got it down to six with 4:36 remaining, but Howell hit another 3 and the Tigers didn't have time for a comeback.
Tasmin Mitchell tied a career high at 23 to lead LSU.
Davis, who was averaging 18.5 points and a league-leading 10.3 rebounds, finished with 13 rebounds but was 2-of-10 from the field.
This was only the second time this season Davis was held in single digits. He had eight points at Washington, a loss for LSU.
Lofton had eight points off one 3-pointer and five free throws.
Lofton started the game and was greeted with loud cheers when his name was announced in pre-game introductions.
He made an immediate impact, getting fouled by Garrett Temple while attempting a 3 on the Vols' first possession. He made all three free throws and had an assist on Tennessee's next basket. Lofton rested often and played 21 minutes.
LSU won last year's meeting in Baton Rouge, when Lofton was held to a season-low two points on 1-of-7 shooting from the field.
Tennessee led by as many as 10 in the first half, the last time at 34-24 with 3:37 left.
LSU responded with a 10-2 run. The Tigers had three straight baskets and then made 4-of-6 free throws in one possession. LSU was fouled on two rebounds off misses that kept them at the line and only took 2 seconds off the clock. Tennessee fans booed loudly.
Mitchell cut it to 36-34 with 29.5 seconds left, but Tennessee ended the first half with JaJuan Smith's three-point play for a 39-34 lead at the break.
The Tigers have not won since beating Mississippi 62-55 on Jan. 17.
LSU finished with 20 turnovers, 15 coming on steals by Tennessee. JaJuan Smith had five steals. Several of the turnovers were on LSU's inbounds play under the Vols' basket.
Florida is the only other SEC team to be undefeated at home this season.