The Hogs made an amazing 16-0 run over the next 4:57, tying the score at 68 with 2:08 left, only to see the Vols produce the game's final six points and prevail 74-68.
The victory sends Tennessee (19-13) against Florida (24-6) in second-round play Friday night at 7:30. Arkansas (18-13) appears likely to land in the National Invitational Tournament.
After shooting 56.9 percent (29 of 51) in the game's first 33 minutes en route to the 68-52 lead, Tennessee sank just one of its final 11 shots. Arkansas, conversely, heated up dramatically.
Arkansas scoring leader Rotnei Clarke, held without a basket in the first half, scored on a drive, a 3-pointer and two free throws during the 16-0 explosion that tied the score at 68.
Just when it appeared the Vols were going to suffer one of the greatest meltdowns in program history, however, they got two big plays by seniors. First, Brian Williams made a layup off a beautiful assist by freshman Tobias Harris to put Tennessee on top 70-68 with 54.9 seconds left.
Then senior point guard Melvin Goins stole the ball from Arkansas's Julysses Nobles, setting up two Harris free throws that padded the lead to 72-68 with 33.8 seconds left.
Goins missed the front end of a one-and-one with 18.5 seconds remaining but hit a pair of free throws with 2.7 seconds left to secure the final margin.
Although the Vols appeared to relax a bit after building the 16-point lead, head coach Bruce Pearl preferred to credit Arkansas for its dramatic comeback.
"You can see that Arkansas is a very dangerous team. They've got a lot of toughness and grit, with Rotnei Clarke and (Marcus) Britt knocking down some big shots. They hit a barrage of 3-balls there late. They didn't panic, didn't feel like the game was over. I would give them great, great credit for coming back on us."
Harris hit 7 of 13 field-goal tries and led the Vols with 20 points. He scored 16 in the first half before Arkansas adjusted and limited him to four second-half points.
"The second half I thought they keyed in on me a little bit more," Harris said. "I just tried to make plays, get other guys going and do what I had to do for us to win the game."
"Tobias Harris played like an All-American," Pearl said. "He's got great confidence because nobody in this country works harder than he does to prepare. It was obvious that he was the dominant player on the floor tonight."
Goins, playing through a flu-type virus, hit 5 of 7 shots and chipped in 12 points.
"This is a tough guy," Pearl said, adding that Goins helped spark the win with "his defense and his ability to make some big plays in there."
First-team All-SEC pick Scotty Hopson got off to a slow start and was benched for much of the first half and the start of the second half. He finished with 8 points, as did replacement Josh Bone.
Senior guards Cameron Tatum and Bone did a spectacular defensive job on Clarke, especially in the first half when he went 0 for 6 from the field and 0 for 4 from 3. Clarke finished with 18 points but made just 4 of 13 shots, including 3 of 10 from beyond the arc. Delvon Johnson added 15 for the Razorbacks.
The Vols dominated play en route to a 37-25 halftime lead. When the 6-10, 270-pound Williams bumped the lead to 56-42 with 12:53 left by draining his first 3-pointer of the year - a 25-footer as the shot clock was expiring - it appeared the Vols could do no wrong. That did not prove to be the case, though.
After shooting just 28 percent (7 of 25) from the field in the first half, Arkansas caught fire late and wound up hitting 66.7 percent (14 of 21) for the second half.
"I thought our first-half defense was tremendous," Pearl said. "The defense down on the other end (after intermission) wasn't as good. That's something we're going to have to fix."