The Tigers played without center Tia Miller, who suffered a dislocated knee cap in a Thursday loss to Tennessee. Her status will be evaluated this week.
Auburn led 25-23 at the halftime thanks to a 15-6 run to close the period. Brackett scored 13 of her points in the first half. AU's defense forced 19 turnovers and AU outrebounded the Lady Kats 32-27.
Kentucky hit 50 percent of its shots to 43.9 for the Tigers, who nailed 18-22 free throws. UK was 8-9 at the foul line. UK hit 6-13 treys while Auburn made just 2-10.
Smith led Auburn with 16 points and Keisha Johnson added 14. Le'Coe Willingham added nine points and a team-high eight rebounds.
Kentucky regained the lead at 34-33 with 13:29 remaining, but then the Tigers went on a 19-3 run led by Smith. The Tigers led 52-37, but had to hold on for a four-point victory.
Sese Helm led Kentucky in scoring with 18 points and Rita Adams added 17.
"It's a great accomplishment by a team that was shorthanded today," AU coach Joe Ciampi said. "That's the character of this team. I'm so proud of them for bowing up today and playing the defense they did. That was the key today. Our heart and soul was in that defense and we broke them down every which way."
Auburn returns to action on Thursday to face eighth-ranked Georgia at Beard-Eaves Memorial Coliseum. Tipoff is 7 p.m.
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