The Crimson Tide (16-14, 6-10 Southeastern Conference) snapped a four-game losing streak to its in-state rival in a game that was close most of the way.
The Tigers (15-16, 6-10) shot just 35.5 percent, making 22 of 62 attempts.
The Tide broke open a one-point game with a 24-10 run to take a 61-47 lead with 2:32 left on a basket and free throw by Torrance, who also had six assists. Hines and Mitchell combined for 13 points during the surge, almost all of them coming around the basket.
Chris Hines added 13 points for the Tide.
Tay Waller led Auburn with 22 points to continue his recent hot streak. He made 4 of 12 3-pointers.