The win, Tennessee's seventh in a row, moves the eighth-ranked Vols to 15-2 overall and 3-0 in SEC play. The loss drops Bama to 11-7 and 1-3.
Tennessee shot just 39.3 percent (22 of 56) from the field and 30 percent (3 of 10) from beyond the arc. The Vol defense saved the day, however, limiting the Tide to 37.9 percent (22 of 58) from the field and 26.7 percent (4 of 15) from 3-point range.
"It was a good, solid team defensive effort," UT coach Bruce Pearl said on his post-game show, "and that's what you've got to do to win on the road."
After losing at Coleman Coliseum in 2006, Pearl has won on each of his two subsequent visits - 2008 and 2010. Prior to his arrival, the Vols had dropped 16 of their previous 17 games in Tuscaloosa.
Tuesday's game looked like another likely loss for a while. Chism was whistled for two early fouls and played just 5 first-half minutes. He picked up foul No. 3 in the second half and went to the bench again. With Tennessee clinging to a 49-44 lead and less than 8 minutes to go, however, the 6-9, 245-pounder took over the Vol scoring load ... and the game.
He hit a layup with 7:13 to go and was fouled, with the free throw boosting Tennessee's lead to 52-44. After a 3 by Alabama's Charvez Davis narrowed the gap to 52-47, Chism scored inside again with 6:15 to go. Senario Hillman scored for the Tide but Chism responded with a breakaway bucket that gave Tennessee a 56-49 lead with 3:52 remaining.
A three-point play by JaMychal Green and a free throw by Mikhail Torrance narrowed the gap to 56-53 but Chism answered by scoring his fourth consecutive UT basket, bumping the lead to 58-53 with 1:06 to play.
After a pair of Bobby Maze free throws, Chism sealed the deal by hitting two foul shots that put the Vols on top 62-53 with 24.2 seconds left. After a 3 by Bama, Maze added a free throw to secure the final margin.
Chism wasn't the only key for the Big Orange. Sophomore guard Scotty Hopson scored a team-high 17 points and freshman Kenny Hall came off the bench to contribute a double/double (12 points, 10 rebounds).
With Chism sidelined by foul trouble, Hopson kept UT in the game in the first half. He produced 11 of Tennessee's final 15 points of the half - scoring on three drives, a 3-pointer and two free throws - as the Vols went to intermission down 25-24.
After Bama scored the first basket of the second half to go up 27-24, Tennessee made a 20-6 run that produced a 44-33 lead with 11:22 to play. Hall sparked the spurt with a putback, a layup and a follow dunk.
Bama clawed back, however, outscoring the Vols 11-5 over the next four minutes to pull within 49-44 and set up Chism's late heroics.
The athletic Tide outrebounded Tennessee 39-37 and blocked eight Vol shots but just couldn't make the key plays in the clutch situations.
"Alabama certainly could've beaten us tonight," Pearl said. "The fact that, with Wayne Chism on the bench in foul trouble, we only went down one at half was a real key. Early in the game we weren't playing very well defensively and they got a lot of good looks but didn't make 'em. They could've run us out of the gym early."
Green led Bama with 16 points and 12 rebounds. Tony Mitchell added 11 points. Tennessee totally shut down the Tide's leading scorer. Torrance, who averages 15.9 points per game, made just 1 of 9 floor shots, finishing with more turnovers (4) than points (3).
"He's the key," Pearl said of Torrance. "He's the guy they really need. We guarded the ball screen and we just wouldn't let him get to the ball screen. We overplayed his left hand dramatically and provided help with the ball-screen defender. We built a wall on him - that's what you've got to do against him - and it was very, very effective.
"That was probably the biggest key to the game."