LaKeisha Johnson added 12 points and five rebounds and Le'Coe Willingham contributed 11 points and a team-high nine rebounds. Tia Miller contributed nine points and six rebounds for Coach Joe Ciampi's team.
UAB, which falls to 4-2, was sparked by Deanna Jackson. She scored 18 points and pulled down 19 rebounds.
Auburn outshot the home team 44.7 percent to 36.7 percent and really put the defensive clamps on the second half, limiting the Blazers to 27.3 percent shooting.
"We put together a great, great effort defensively," Ciampi said. "We are maturing as a team. We learned in the Syracuse game and this one on the road. You have to value every possession and make defensive stops." Auburn was outrebounded 40-30, but overcame that by hitting 16-22 free throws while UAB could make just 10-19.
Johnson hit two free throws with two seconds to play to clinch the 62-57 victory. She got the free throws after UAB's Jackson attempted to call a timeout when her team had none left, resulting in a two-shot technical foul.
Auburn led 32-29 at halftime and took its largest lead at the 13:35 mark with a 43-33 advantage. UAB narrowed the lead to two points with 12 seconds left on a Jackson three-pointer. Auburn's Smith then hit the second of two free throw attempts to give Auburn a 60-57 lead.
Auburn returns to action at home with a 7 p.m. game vs. Tennessee State.