Wall lived up to his billing in his first appearance at Madison Square Garden, overcoming first-half foul trouble and dominating the game over the final 7 1/2 minutes.
The Wildcats (9-0) moved John Calipari closer to one of the icons at the school that has more wins, 1,996, than any other program. The only coach to have a better start to his career at Kentucky was Adolph Rupp, who started 10-0 in 1931.
There were two totally different halves played in front of the crowd of 15,874, which seemed split down the middle.
Jerome Dyson had 17 points for the Huskies (6-2), who finished 14 of 24 from the free throw line, including 2 of 4 in the final 3 minutes.
After a first half of runs and big swings, neither team had a lead of more than five points over the final 7 minutes.
Wall, the 6-foot-4 guard who has drawn raves in his freshman year as Calipari tries to lead Kentucky back after two disappointing seasons under Billy Gillispie, scored almost every way possible in his game-closing spurt.
His three-point play on a breakaway dunk gave the Wildcats a 54-47 lead with 7:16 left. Stanley Robinson, Connecticut's skywalking forward, finally became a factor for the Huskies, scoring six straight points. When Gavin Edwards scored on a break dunk with 4:24 to play, Connecticut was within 56-55 with 4:24 to go.
Kemba Walker, who had 12 points and six assist for the Huskies, gave them their final lead of the game on a jumper with 1:12 left.
Wall put Kentucky ahead for good on a three-point play after he drove to the basket that made it 63-61 with 30 seconds left.
Connecticut called two timeouts then went for the tie as Walker drove and there was a tip by the Huskies as well. But Walker was forced to foul on the rebound, and Ramon Harris made one of two free throws with 13 seconds left.
Edwards missed a forced 3-point attempt, and Walker couldn't get a shot off from the corner in time after coralling the rebound.
Patrick Patterson had 16 points for Kentucky, and DeMarcus Cousins added 10 points and 10 rebounds.
Kentucky had a start no coach can even dare dream about. The Wildcats scored the game's first 12 points and Connecticut coach Jim Calhoun used two 30-second timeouts before the 16-minute media timeout.
Wall lived up to his billing in his first appearance at Madison Square Garden, stealing the ball twice to lead to Kentucky baskets, throwing down a thunder dunk on the break, hitting a jumper and then scoring on a drive to cap the opening run.
The Connecticut fans had their chance to make some noise in a hurry. After going 4:18 without a point, the Huskies were on a 10-0 run of their own as Dyson starting getting inside for good looks. Unlike the Wildcats, the Huskies didn't let up.
Connecticut took its first lead at 19-18 on a free throw by Dyson with 8:17 left, and the Huskies kept it up, going ahead 26-18 on a drive by Walker with 6:30 left. That completed a 26-6 run during which Wall picked up his second foul with 7:56 to go. He didn't return the rest of the half, which finished with Connecticut leading 29-23.