The Tigers (14-11, 4-8 Southeastern Conference) used a 14-4 run midway through the second half to break open a four-point game and easily avoid a season sweep by their rival.
Hargrove made 9-of-12 shots and topped his previous best of 13 points by halftime in just his second start of the season.
Quan Prowell added 22 points and nine rebounds despite playing much of the game in foul trouble. He made 4-of-6 3-pointers before fouling out late.
Quan Prowell played big in the post despite battling through foul trouble.
Alabama (14-13, 3-9) fell into a tie with LSU for last place in the SEC Western Division with its fourth loss in the past five games. Auburn, which had dropped six of its last seven, now shares third place with Mississippi.
They had fallen by 20 points earlier this season at Alabama.
This time Hargrove came out hot, scoring 11 points in a three-minute span of the first half after replacing DeWayne Reed in the starting lineup. Undersized Auburn also kept Alabama's Richard Hendrix in check most of the game, making it hard for the Tide to get him the ball inside.
Alonzo Gee led Alabama with 18 points and nine rebounds, while Hendrix finished with 16. Both were contained until the final minutes when the game was already decided. Hendrix finished with seven rebounds, three below his league-leading average.
Mykal Riley added 15 points and 10 rebounds and his four 3-pointers gave him 12 for the past two games.
The Tigers' decisive spurt gave them a 68-54 lead with 7:41 left on Prowell's short jumper. Alabama quickly cut the deficit to eight but Barrett answered the short run with a 3-pointer and the Tide never got back within single digits.
The Tide had taken a 40-39 halftime lead on Brandon Hollinger's drive to the basket with 5 seconds left. Alabama had used a 20-3 run to go up by as many as 10 points, but Hargrove's 11-point scoring binge helped the Tigers come back.