Playing its first game of the season on an opponent's home court, Kansas (11-0) won for the fourth straight time without preseason All-America Wayne Simien, who is out following surgery on his left thumb. Included in that stretch are wins over two Top Ten teams, Georgia Tech and Kentucky (10-2).
The loss snapped Kentucky's six-game winning streak.
Giles, a freshman starting in place of Simien, went 5-of-5 from the field and finished with 10 points, six rebounds and two blocked shots. Moody, a junior walk-on, had 11 points and seven rebounds, while Kaun, who didn't play in Kansas' last game against Texas A&M, added seven points.
The win was only the Jayhawks' fourth in 23 meetings with Kentucky and their first in 11 tries against the Wildcats in Kentucky.
Kansas held its biggest lead at 52-44 with 6:12 left, but a 9-0 Kentucky run, capped by a driving, off-balance layup by Patrick Sparks, put the Wildcats up 53-52 with 3:54 left.
Aaron Miles scored his only basket of the game to regain the lead for good for the Jayhawks, who won despite committing a season-high 21 turnovers.
Kansas led 58-56 and had the ball when Miles fell down while dribbling and being harassed by Sparks. The ball bounced to Michael Lee, who made a 3-pointer with 30 seconds left.
Miles and J.R. Giddens each made two free throws over the final 17 seconds to seal the win.
Kansas finished the game without Giles, who had fouled out, Moody, who injured his ankle, and senior guard Keith Langford, who was hit in the head with 2:45 left and never returned.
Neither team shot well. Kansas was 21-of-53 from the field (39.6 percent), including 4-of-16 from 3-point range. Kentucky fared worse, shooting 21-of-68 (30.9 percent), including 6-of-26 from beyond the arc.
Kelenna Azubuike led the Wildcats with 12 points, but was 4-of-16 from the field. Sparks had 10 points on 4-of-13 shooting. The only consistent offensive threat for Kentucky was reserve forward Bobby Perry, who had 10 points and seven rebounds, both career highs.
Kentucky didn't reach double figures on the scoreboard until 6:42 remained in the first half, but the Wildcats closed the half on a 16-6 run to lead 25-21.
An 8-0 run by Kansas early in the second half put the Jayhawks ahead 40-33 with 13:42 left.
Kentucky is 25-7 all-time at Rupp Arena against higher-ranked opponents.