Fellow freshman Anthony Davis added 18 points, all in the second half, for the Wildcats (13-1) in their annual in-state rivalry game that at times looked more like a free throw shooting contest with 52 fouls.
The Cardinals (12-2) only led at 2-0, but gave Kentucky all it could handle after rallying from an early 15-point deficit before tying it in the second half thanks to Russ Smith, who had a career-high 30 points.
But Kidd-Gilchrist's hustle and Davis' emergence proved to be the difference with rapper Jay-Z, actress Ashley Judd and nearly a dozen NBA scouts on hand.
Kentucky has won 44 straight at home, including 43 in a row at Rupp Arena, for the nation's longest streak ahead of Duke's 43. This one will be remembered after the teams came in with the highest combined ranking in history.
With the game tied at 40 early in the second half, Louisville had a chance to take its second lead but Peyton Siva never hit the rim on an 18-foot jumper.
Kentucky went on a 7-0 run from there, with Kidd-Gilchrist hitting one of two free throws and making a layup on another trip before Davis got to the line and made four free throws over two possessions to make it 47-40.
The battles kept going after the whistle with Davis and Rakeem Buckles tangled up on an out-of-bounds play and Davis pleading for a foul.
On another one, Davis went flying into the crowd trying to make a save and landed on an older woman in the front row. Kidd-Gilchrist came over, screaming, "A.D.! A.D.!" with a smile on his face as he pulled his teammate back toward the court.
Kidd-Gilchrist's three-point play with 3:41 left gave the Wildcats a 61-50 lead, its first beyond double digits since the first half, and Kentucky was never seriously threatened for its third straight win in the series.
Gorgui Dieng, who entered the second half with one foul, picked up three in a span of 2:20 to head to the bench with 16:08 left, but seconds later, Kentucky coach John Calipari picked up a technical foul for his displeasure with the officiating.
Trailing 40-36, Smith hit a 3-pointer and was fouled by Kidd-Gilchrist. He converted it to tie the game with 15:21 left, but Louisville never got over the hump after also rallying from an 11-point deficit before losing against No. 12 Georgetown for its first loss on Wednesday.
Louisville freshman Chane Behanan was the first player to lose his cool in this emotionally-charged matchup of schools separated by 78 miles.
Behanan, recruited by both schools, had already picked up an early foul when he was called for a charge and assessed a technical for his reaction with 16:16 left in the first half.
Louisville opened with a 2-0 lead, but Darius Miller answered with a 3-pointer and Kidd-Gilchrist was the only Wildcat to make a field goal over the next 13:45 as Kentucky feasted at the foul line to build a 31-16 lead.
The only adversity early came when Davis crashed into Russ Smith to draw his second foul and then bowled into associate head coach Richard Pitino, son of coach Rick Pitino, on the Louisville bench midway through the first half.
Trailing by 15 points, Louisville's two Smiths mounted a 13-0 run.
Chris and Russ Smith, who aren't related, scored five points apiece in the spurt that cut it to 31-29 with 2:51 left. Louisville cut it to 34-33 exactly a minute later after a basket by Russ Smith, but Kyle Wiltjer's layup gave Kentucky a 36-33 lead at the half.
Louisville would tie it before 5 minutes passed in the second half, but never could mount a push to take control in one of the most hyped games since the 1983-84 season opener.
In that game, No. 2 Kentucky won over No. 6 Louisville, which marked the start of the annual matchup between the schools following the Cardinals' 1983 NCAA tournament win in overtime over the Wildcats in the regional finals.