The lead swapped hands 12 times during the weekend, including four in Sunday's finale. LSU capitalized on a five-run eighth inning to break a tie and seal the win.
Alabama loss, the Tigers are now a half-game behind the Tide and Ole Miss for the SEC West lead.
"It was a long, hard, tough weekend in the SEC," said LSU coach Paul Mainieri. "I got to give [Tennessee] a lot of credit. They battled us tooth and nail every step of the way."
After Tennessee tied it with two runs in the top of the eighth, LSU answered in a big way.
Jake Fraley got it started with a leadoff walk, and after pinch-hitter Jared Foster struck out bunting, Conner Hale laced a double down the LF line to score Fraley from first for the go-ahead run. That capped off a productive day for Hale, who finished with a season-high three RBI.
"I was just trying to take until I got a strike," Hale said. "He threw me a first-pitch curveball, and I had a feeling he was going to come back with a fastball and I was ready to hit it."
The Tigers poured it on in the rest of the inning, scoring thrice more to pad its lead. Kade Scivicque walked in the at-bat after Hale, and Christian Ibarra laid down a safety squeeze the Vols couldn't field to bring in the run.
Andrew Stevenson was hit by a pitch in the next at-bat to load the bases, and Mark Laird's fielder's choice made it 7-4. A wild pitch made the lead four, and Alex Bregman tacked on the fifth with a single to left.
The LSU offense made a habit of striking back when the Vols struck first. In all three innings Tennessee scored on Sunday, LSU answered with runs in the bottom of the frame.
"Us hitters knew that we were going to be in for a challenge this weekend, and we'd have to match them offensively," Bregman said. "We knew they're a good offensive team…and it lit a fire for us."
That five-run outburst was a much-needed reply after LSU blew a two-run lead in the top half of the inning.
Kurt McCune started the inning on the mound after surrendering a pair of runs in a third of an inning Saturday. The Vols had similar success against him Sunday, recording a double and single in the first two at-bats of the inning to cut the deficit at the time to 4-3.
After a sacrifice bunt and an error by Ibarra, Tyler Schultz tied it with a sacrifice liner to center.
"Tennessee's the best hitting team we've played all year," Mainieri said. "They were really tough outs, and they've got some guys that are real threats."
LSU had taken the lead with three runs in the fourth and fifth innings. Fraley brought in one with a groundout in the fourth, and Hale drove in another with an infield single two at-bats later.
A wild pitch in the fifth inning gave LSU a 4-2 lead at the time.
The two teams matched runs early in the game, as Tennessee jumped out to a one-run lead in the second with a sacrifice fly by Will Maddox. LSU answered with a sacrifice fly of its own in the bottom of the inning.
Tennessee regained the lead in the fourth with a single by Derek Lance, his sixth of the series.
Next up for the Tigers is a midweek contest against Alcorn State on Tuesday. They'll hit the road next weekend for a three-game set against Texas A&M with hopes of extending the series win streak to five.
"Anytime you win one in the SEC, you put it in your back pocket and take it home with you," Mainieri said. "Games are hard to win in this league."