The Bulldogs (35-19-1, 20-9-1 Southeastern Conference) took a 9-4 lead in the fourth inning, scoring six runs.
But Alex Avila hit a solo homer in the fifth for the Crimson Tide (32-24, 16-14). Then Alabama added six runs in the following inning to claim an 11-9 lead, highlighted by Bentley's two-run single.
Georgia tied the game at 13-13 in the eighth on O'Bryan's run-scoring single and a three-run homer by Bryce Massanari. But the Crimson Tide scored two go-ahead runs and Bentley's run-scoring single to pull away in the ninth.
Austin Graham (6-1) allowed four runs and three hits two innings for Alabama.
Bulldogs reliever Joshua Fields (2-2) took the loss.