Emeel Salem walked to lead off the 10th inning and came around to score on a single from freshman Jake Smith, who returned to the lineup this weekend after missing five games with a strained knee.
Smith had a grand slam on Saturday night among his three hits to blow the game open for Alabama.
Alabama starting pitcher Austin Hyatt threw six innings allowing only three hits and one earned run, while striking out seven. Relief pitcher Josh Copeland gave up two runs on two hits in the seventh inning.
The Tide was held scoreless until the sixth inning when Greg Pamil scored on Jeff Texada's single up the middle for a 1-0 lead.
Tommy Hunter pitched in relief for the second straight game, working the ninth inning before Bernard Robert came in to pitch in the 10th.
Alabama will play its first game away from Sewell-Thomas Stadium on Tuesday, against Southern Miss in Jackson, Mississippi.