DeWayne Reed cut Kentucky's lead to 70-67 with two free throws with 1:08 left, then Eric Bledsoe missed an open 3-pointer and the ball went out of bounds to the Tigers (9-9, 0-3) with 37 seconds to play.
Reed missed a 3 and the Wildcats' DeAndre Liggins grabbed the rebound and was fouled. Kentucky inbounded the ball to Wall, who was quickly fouled and made the free throws that continued Kentucky's best start in 44 years.
The Wildcats had shut down Auburn after Frankie Sullivan's 3-pointer tied it at 60 with 8:23 left. The Tigers went 4 minutes without scoring as Kentucky used stingy defense to overcome some missed drives and turnovers
DeMarcus Cousins, a native of Mobile, had 16 points, 11 rebounds and four blocked shots in his first game back in his home state. He was 5 of 6 from the field and 6 of 10 from the free throw line.
Wall finished with 13 points and four assists. He gave a slight smile after hitting his first free throw in the final seconds to make it a two-possession game, then calmly made his second.
Fellow freshman Eric Bledsoe, who is from Birmingham, also had 13 points, while Patrick Patterson finished with 12.
Reed led Auburn with 19 points and six assists despite missing his first 10 shots. He kept firing away, taking 25 shots and making seven.
Sullivan made 3 of 5 3-point attempts and scored 10 of his 15 points in the second half. Lucas Hargrove added 10 points.
Auburn has lost 11 straight games against top 10 teams, including two in three days. The Tigers were routed 81-55 Thursday night at No. 9 Tennessee, but followed with a much stronger showing.
It was another close call for Kentucky, the fifth time the Wildcats have won either by five points or less or in overtime.
Kentucky committed 16 turnovers but shot 51 percent and capitalized on repeated trips to the free throw line. The Wildcats attempted 35 free throws, making 23.
All but eight came in the first half, when Kentucky built a 39-26 lead. Auburn shot 29 percent in the half and was out-rebounded 27-14.
The Tigers bounced back to hit 16 of 29 shots in the second half.