Kansas' Tyshawn Taylor stole the ball and dished it to Brady Morningstar, who hit a 3-pointer with 1:14 left to cut Tennessee's lead to 71-68.
Skylar McBee, one of three walk-ons who played for Tennessee, answered with his own 3 as the shot clock expired.
Sherron Collins, who bailed the Jayhawks (14-1) out of a near loss to Cornell on Wednesday with a career-high 33 points, couldn't help this time, missing three shots before time expired. Collins led Kansas with 22 points.
Kansas couldn't find its composure in front of 21,936 screaming Tennessee fans at a sold-out Thompson-Boling Arena, which was hosting a No. 1 team for the first time. The Jayhawks turned the ball over 16 times, while Tennessee (12-2) had only eight turnovers.
The loss leaves No. 2 Texas and No. 3 Kentucky as the only unbeatens in Division I and it was the fourth this weekend by a Top Ten team, joining No. 4 Purdue, No. 5 Duke and No. 8 West Virginia.
It was the Vols' first game after coach Bruce Pearl dismissed Tyler Smith on Friday, a week after the senior was arrested on misdemeanor gun and drug charges. Tennessee was also playing without Cameron Tatum, Melvin Goins and Brian Williams, who were arrested Jan. 1 with Smith.
But Tennessee, who had already lost two players before the season started, played even more shorthanded than that. Starters Wayne Chism and J.P. Prince found themselves in foul trouble early and both spent more than half of the game on the bench.
The Vols showed they could play defense even playing three walk-ons and two freshmen at the same time. They limited the Jayhawks, who entered the game shooting 51.3 percent from the field, to an uncharacteristic 37.7 percent. Tennessee shot 48.1 percent, the best by a Kansas opponent this season.
Bobby Maze added 16 points for Tennessee, and Renaldo Woolridge had 14 points and eight rebounds playing in place of Smith.
Kansas shut down Tennessee's game in the paint early until Woolridge hit three consecutive 3-pointers — all from the same spot on the court — as part of a 14-2 run by the Vols.
From there the Vols found the lane a little more accessible. Hopson drove to the basket for a layup at the end of the run to give Tennessee a 27-21 lead. Tennessee finished with 30 points in the paint compared to Kansas' 20.
Maze gave Tennessee its first lead with a layup around big man Cole Aldrich that made it 23-21 with 5:59 in the first half. Kansas would only lead once more, on an alley-oop dunk by Taylor with 18:03 in the second half that made it 37-36.
Taylor had 13 points, and Xavier Henry added 10. Aldrich grabbed 18 rebounds as Kansas outrebounded Tennessee 42-35.
Kansas entered the game averaging 27.6 points more than its opponents and having dominated then-No. 18 Temple, its only other Top 25 opponent, 84-52 on Jan. 2.
Kansas won the only other meeting between the schools, a 92-58 victory at Kansas on Jan. 3, 2009. The Jayhawks dominated that game as Collins and Aldrich combined for 48 points. Smith led the Vols with 21 points and nine rebounds.
It was the second consecutive win for Tennessee over a No. 1 opponent. The Vols last faced the No. 1 team when it won 66-62 at Memphis on Feb. 23, 2008, a win that vaulted them to their first, albeit brief, No. 1 ranking.