The Longhorns had won 33 consecutive non-conference home games before the Vols shocked the 13,682 at the Erwin Center Saturday afternoon.
"We'd heard we'd lose the whole week,'' senior point guard C.J. Watson said. "Everyone thought this was our first big test, and we'd fail.
"But we knew we were going to win coming in.''
Tennessee (6-0) played like it, taking Texas (8-2) by the horns early on and not relenting through 40 minutes of play.
The Vols built a 15-5 lead in the midst of a 13-0 run, and the Longhorns failed to draw within single digits the rest of the way.
"I don't know that we are this good,'' Tennessee coach Bruce Pearl said. "I know we played a great game.''
Chris Lofton led Tennessee with 21 points and Watson added 17. Three others Major Wingate, JaJuan Smith and Andre Patterson scored 12 apiece for the Vols.
Tennessee held a 48-28 advantage at halftime, and the lead swelled to 25 points with 11:48 left when Smith hit one of his four 3-pointers to put the Vols up 67-42.
Texas didn't get back within 20 until Kenton Paulino knocked down a 3-pointer that made it 79-60 with 4:47 left. Paulino's 3-pointer came during a 12-0 run that brought the Longhorns to 79-68 with 2:47 remaining.
The Vols showed no signs of panic, however, going 12-for-12 from the free throw line over the final 2:13.
The normally stoic Watson smiled and laughed as he stepped to the line with time winding down.
"They were fouling the wrong person,'' said Watson, who has hit 85 percent of his free throws this season and was 6-of-6 from the line Saturday. "I don't think they took us seriously. This game shows how serious we are.''
The win marks the first time Tennessee has beaten a top-10 team on the road since beating No. 9 Florida in double overtime, 81-79, on Jan. 18, 2000.
Texas played without senior forward Brad Buckman, who suffering a strained calf in a loss to Duke last Saturday. Things got worse for the Longhorns when starting point guard Daniel Gibson was knocked out of the game with a mild concussion after a loose ball scramble with 10:26 left in the opening half and the Vols up 26-10.
A.J. Abrams, Gibson's replacement, came off the bench to score 19 points while P.J. Tucker led Texas with 20 points and 11 rebounds. Tucker was the Longhorns' only consistent scoring threat inside.
It was by design.
The Vols played smothering half-court defense, forcing 22 turnovers and muscling up with physical play in the paint.
The aggressive strategy led to Wingate and Ryan Childress fouling out and Andre Patterson and Lofton finishing with four fouls each.
But that physical interior play also took the Longhorns out of their game.
"I wasn't intending to use all those fouls,'' Pearl admitted. "I got a little nervous.''
The rest of Pearl's game plan, however, worked to perfection, particularly the adjustment Tennessee made to its press.
"We were always in some form of full-court pressure; we just didn't trap as much,'' Pearl said. "Trapping would give them spacing, and Texas is a great fast-break team.''
The Longhorns struggled to find offensive rhythm. They scored 11 points off 10 UT turnovers and got six points off fast breaks. Tennessee scored 34 points off turnovers and 14 on the break.
"When you turn it over and give a team like that an open court, they'll find what they're looking for, and they did,'' Texas coach Rick Barnes said.
"I think our guys gave it their all, but Tennessee just played good basketball,'' said Texas center LeMarcus Aldridge, who had 15 points and nine rebounds. "They shot the ball well, doubled the posts well, and they took our point guard out. They just took care of business.''
Aldridge had Texas' only dunk in the game, but it was just one of just five field goal attempts he managed against an inspired Wingate.
"I felt like I could take anybody if I wanted to,'' Wingate said. "He (Aldridge) only has two or three basic moves. I just had to motivate myself.
"You know, a lot of stuff changed this year when coach Pearl came on the scene,'' Wingate said. "He gave us a lot of heart, and he's going to lead us to a lot of victories.''