The Tigers fell to 0-3 in SEC play and 8-6 overall while Tennessee improved to 11-5 overall and 2-1 in league games.
Chris Denson led all scorers with 24 points, but Tennessee had more balance with five players scoring in double figures.
The Tigers were down 68-63 with 2:43 to play after Denson scored a basket and a free throw, but the home team made key defensive stops at crunch time and hit its free throws to hold on for the victory.
Tennessee led the entire game building a 16-6 edge less than eight minutes into the action at Thompson-Boling Arena, where the Tigers were looking to win for the first time since the 1998 season.
Auburn junior guard K.T. Harrell looks for room to score vs. the Vols.
The Tigers cut the lead to 23-19 on a three-pointer by Tajh Shamsid-Deen, but the Vols built the margin back to double figures at 31-21.
The Tigers cut that lead in half by intermission to trail 33-28 at the break.
Shamsid-Deen hit a three to start the second half, cutting the margin to two points, but that was as close as the Tigers could get.
"We couldn't get the stops when we needed them," Auburn coach Tony Barbee said. "Their big guys imposed their will on my team in the paint. We gave ourselves opportunities again to win on the road, but we just came up short.
"We got out-rebounded tonight and they went to the foul line at a higher clip than we did," the coach added.
"We just have to stay together and keep fighting," Barbee said. "I am confident this team will do that." The Tigers have dropped 13 consecutive SEC games going back to last season.
Chris Denson played a team-high 36 minutes vs. the Vols.
Denson hit 10-18 field goals and was joined in double figures by 15 points from K.T. Harrell and 10 from Shamsid-Deen. The fourth leading scorer for the Tigers, Asauhn Dixon-Tatum, finished with six points and a team-high eight rebounds.
Tennessee also outshot the Tigers 51 to 41 percent from the field. That, and the rebounding margin, were a major difference in the game along with attempts at the foul line.
The Tigers hit 8-17 three-pointers and 9-14 free throws. Tennessee hit 3-9 threes and 23-30 free throws.
The Vols turned the ball over 15 times, three more than the Tigers.
Halftime Numbers: The Tigers trailed 33-28 with the Vols out-shooting the visitors. UT hit 14-29 field goals (48.3 percent) while Auburn hit 10-30 (33.3 percent) from the field. The Tigers were 3-9 on threes and 2-2 at the foul line. The Vols hit 2-7 threes and 3-5 free throws. Tennessee led in rebounding 21-16 and turned the ball over nine times, one more than Auburn. Harrell led the Tigers in scoring in the half with eight points.
Worth Noting, Part 1: Allen Payne, who has been trying to recover from a hamstring injury, started but struggled. The senior forward was 1-7 from the field and finished with four points and four rebounds.
Worth Noting, Part 3: Freshman forward Alex Thompson, who joined the team as an invited walk-on out of Houston Academy in Dothan, has been put on scholarship for spring semester. He played 10 minutes and scored three points and added two rebounds vs. the Vols after scoring eight points vs. Missouri.
The Tigers return to action with a 3 p.m. CST home game on Saturday vs. the Florida Gators.