The win gave Kentucky its 12th 30-win season - the most by any school - and the Wildcats' first since 2003 when they went 32-4. It's also the fifth straight such season for John Calipari and seventh overall to tie him with Connecticut's Jim Calhoun for third-most among coaches.
Kentucky (30-2) will play either No. 15 Tennessee or Mississippi in the semifinals Saturday looking to add a 26th tournament title to the 44th regular-season championship.
Patrick Patterson scored 20 and Eric Bledsoe 10 for Kentucky. DeMarcus Cousins, who had 18 double-doubles this season averaging 15.6 points and 10 rebounds per game, finished with seven points and eight boards.
Mikhail Torrance led Alabama (17-15) with 20 points. JaMychal Green had 14 and Tony Mitchell 10.
The Tide just couldn't match Wall or the crowd in essentially a road game in Rupp Arena South as fans painted the inside of Bridgestone Arena blue.
Kentucky improved to 112-22 in this tournament and 9-1 in Nashville. The Wildcats now are 4-1 against Alabama in the quarterfinals, a program that ranks second only to Kentucky in the number of tournament wins and titles in the league.
The Wildcats lead the series 100-35, including nine of the last 11 and five straight, even though fans didn't get to crank up into a full roar until the second half. That's when Wall took over and put Kentucky ahead to stay with his spurt, the last a three-point play to put the Wildcats up 43-42, their first lead since they were up 8-7.
The freshman had brought the fans to their feet with a driving layup, and waved his arms to urge them to turn up the volume as he went back down the floor after his next inside bucket. He followed up with another layup to tie it at 42 with 13:51 remaining, drawing the foul that let him put the Wildcats ahead with the free throw.