Wyoming was in the midst of a 19-2 run in the first half when Tennessee coach Bruce Pearl called a rare timeout.
"You probably noticed our circle was a little tighter during that timeout,'' UT center Wayne Chism said. "We came in the huddle, and we realized we needed that. We hadn't been behind by 10 points all year.
"Coach (Pearl) had faith in us the whole time.''
The ninth-ranked Vols (8-1) scored a 77-58 victory over Wyoming (5-5) before an announced crowd of 17,274 at Thompson-Boling Arena on Tuesday night.
But not before the Cowboys shot out to a 7-0 lead and went up 35-25 at the 5:47 mark of the first half.
The Vols rallied to take a 42-41 lead into intermission and wore down Wyoming with their depth and staunch half-court defense.
The upset-minded Cowboys, led by Afam Muojeke's 15 points, trailed 48-47 with 16:51 left when Tennessee kicked it into another gear with an 11-2 run.
The Vols clamped down defensively and got more aggressive going to the rim in the midst of their run. Melvin Goins capped it with a short pull-up jumper that gave the Vols a 59-49 lead with 13:46 left.
Wyoming didn't draw closer than eight for the remainder of the game, managing only one field goal over the final 13 minutes.
"That second-half defense, we held them to five field goals, 17 points, outrebounded them; that's how you win games,'' Pearl said. "I think we learned a lot. We stepped up, so I'm pleased.''
Scotty Hopson led the Vols with 14 points, Chism had 13 points and Tyler Smith had 10 points and six rebounds.
"We shot 4-of-20 from three(-point range), and last year we would have pulled out the win, but it would have gone right down to the final minute,'' Smith said. "Playing that defense opens up more run-outs, dunks and possessions.
"We just had to man-up.''
Brian Williams and J.P. Prince provided pivotal minutes off the bench. Williams had seven rebounds to go with nine points, and Prince recorded six assists while making a game-high four steals.
"He (Prince) is starting to come, starting to get in the flow, taking the charges and joining Tyler in that high assist/turnover ratio,'' Pearl said. "Getting 12 assists from Tyler and J.P., that's why I talked to (associate head coach) Tony Jones about keeping Tyler or J.P. on the floor the whole time.''
Renaldo Woolridge made the most of his eight minutes with four rebounds, drawing praise from Pearl for providing quality time that gave Smith an opportunity to receive a much-needed rest.
The Vols play at Southern Cal (4-4) at 4:30 p.m. EST on Saturday.
History Lesson: The first meeting between the Vols and Wyoming took place in December 1958 in the Armory-Fieldhouse, which later became Stokely Athletics Center.
Kenny Coulter made a basket to give UT a 72-71 win. Coulter was the timeout coordinator for the game Tuesday night.
Hospital Visit: UT players and coaches will visit patients at the UT Medical Center's Cancer Institute this morning in conjunction with the OUTLIVE initiative founded last year.