The Tigers (9-13, 3-6 Southeastern Conference) snapped a six-game losing streak despite managing just 13 points in the first half.
It was a season-low in points for Alabama (14-8, 6-3), which had won six of seven games and five straight in the rivalry. The Tide's previous low was 50 points.
Payne scored nine points in the second half. Wallace, who was averaging 3.6 points, matched his season high -- all in the second half.
Auburn mounted the comeback even with leading scorer Frankie Sullivan missing his first 11 shots in a 1-for-13, four-point performance.