Augustus, a senior who is the reigning National Player of the Year, made the most of her final performance in the arena by scoring 32 points on 10-of-20 shooting.
She was one point shy of her career high of 33 set in 2004 against Baylor.
She made it interesting in the final moments, as the LSU career free-throw percentage leader missed consecutive free throws with 6.2 seconds to play that would have put the game on ice.
However, she dogged Shana Zolman down the court and blocked her three-point attempt from 28 feet with two seconds to play and made her latest mark on women's college basketball.
On the previous Lady Vols possession, Augustus blocked a Dominique Redding three-point attempt from the baseline that would have tied the game. She picked up the rebound and was fouled with six seconds to play.
In their 17th try, LSU (21-1, 9-0 SEC) earned the first win in the history of the women's program over Tennessee in Knoxville.
Tennessee (21-3, 7-2 SEC) lost to an SEC opponent in Knoxville for the first time since Dec. 8, 1996, when Georgia defeated the Lady Vols, 94-93, in overtime.
Behind Augustus, Scholanda Hoston came on strong with 18 points on 8-of-12 shooting. Fowles, her back hurting and in foul trouble early, came back to score 10 points and grab 15 rebounds.
LSU shot 45.8 percent from the field (27 of 59), adding 15-of-22 free throws.
The Lady Vols were led by redshirt freshman phenom Candace Parker who had 23 points on 9-of-17 shooting. Forward Tye-sha Fluker added 14, while Alexis Hornbuckle had 11 points, six assists and six rebounds.
The Lady Tigers scored the first six points of the game and opened an 11-1 lead in the first 3:36, on 5-of-7 shooting. In that run, Tennessee missed its first four shots before Parker scored the Lady Vols' first basket with 16:10 to play.
LSU maintained the lead for the first eight minutes, as Augustus made her first three shots and scored seven points to give the Lady Tigers a 19-6 advantage.
After making only 2-of-10 attempts to start the game, shots began to fall for the Lady Vols over the next four minutes and the play also got more physical.
With Fowles on the bench for eight minutes in the half, first with a back injury and then with two fouls, the Lady Vols used an 18-6 run to trim the margin to one point, 25-24, with five minutes left in the half.
The Lady Tigers would not be shaken, even without the 6-6 sophomore center for the final 5:46. LSU used an 8-2 run over the next four minutes to again push the lead to eight, 32-24, on a three pointer Hoston three pointer made possible by Augustus' dribble penetration.
Augustus scored four straight points in the final minute, but Parker hit a 15-footer as the half ended to keep LSU's lead at six, 37-31.
Each team shot 44 percent in the half, while the Lady Tigers out-rebounded Tennessee, 22-18. Fowles had 11 of LSU's boards.
LSU and Tennessee each turned up the defensive pressure early in the second half, as each made two shots in a combined 17 attempts. LSU led 41-38 with 15:12 to play.
The Lady Tigers were called for consecutive offensive fouls -- one each on Fowles and Williams -- allowing Tennessee to take its first lead of the game, 43-41, on a three pointer by Shana Zolman with 14:15 left.
With Fowles and Thomas on the bench, LSU went scoreless for more than four minutes. However, the Lady Tigers hung tough defensively to stay within four, 46-42, at the 11:52 media timeout.
Coming out of the break, Augustus began to take over the game, making three straight shots and scoring nine points in a four-minute span to put the Lady Tigers back on top, 54-52.
LSU was able to increase the advantage to five, 60-55, on a 17-foot jumper by White. Tennessee then took advantage of a pair of LSU turnovers to re-take the lead, 65-64, with 3:53 to play.
During the run, Hornbuckle was called for a technical foul for taunting. Augustus made both free throws.
Fowles and Hornbuckle traded baskets before Augustus began her onslaught.
The senior cut to the basket with less than two minutes to play, caught a high pass from Fowles and layed it in without landing to give LSU a lead it would not relinquish, 68-67.
Hoston increased the lead to three, 70-67, when White found her under the goal on an in-bound pass for a layup with two seconds on the shot clock.
A crowd of 15,850 was stunned at the conclusion.
LSU returns home to face Georgia on Sunday at 2 p.m. CT at the Maravich Center.
Lady Tigers break streak- win at UT
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