Curtis' free throws gave the Rebels (19-9, 5-9 Southeastern Conference) a 91-86 lead. But Alabama's Demetrius Jamison hit a jumper to cut the margin to 91-88 with 7.9 seconds left.
That's when things got strange. Senario Hillman came up with a steal for Alabama and missed a 3-pointer. Curtis grabbed a rebound for Ole Miss with 2.5 seconds left, but the game clock suddenly froze.
Players stood around wondering what was going on. Game officials conferred, and after using a stop watch, determined the game ended with Curtis in possession of the defensive rebound.
The bizarre finish overshadowed an Alabama rally that nearly erased a 15-point deficit in the final 2:03.
The Crimson Tide (15-14, 4-10) hit seven consecutive field goals and three free throws before Hillman's final game-tying attempt with six seconds left.
David Huertas 18 points and nine rebounds for the Rebels, who kept their slim NCAA Tournament hopes alive by winning for the second time in the past three starts.
The game was tied 38-38 at halftime.
The Rebels shot 75 percent from the field in the second half, but needed six consecutive free throws by Curtis and Warren in the final minutes to preserve the win.