Bowers hit two early 3-pointers and finished with 20 points and 18 rebounds to lead the Tigers (9-8, 3-3 Southeastern Conference), who won the rivalry game three days after pulling off an upset of No. 23 Kentucky. Canty made 5 of 8 3-pointers and poured in 25 points after scoring 26 against the Wildcats, when he hurt his ankle.
''I thought Bowers was that 6-7 gorilla out there that just was a man,'' Auburn coach Bruce Pearl said. ''Inside and out, he played terrifically.
''Kareem was just Kareem, doing what he does. Those guys just kind of put us on their shoulders.''
The Crimson Tide (10-7, 1-4) led by 10 points in the first half but wound up losing its second straight game since handing South Carolina its first loss of the season.
Retin Obasohan scored 27 points for Alabama, which had three players foul out in the final minutes.
''We didn't do a good enough job containing the basketball, rebounding the basketball,'' Tide coach Avery Johnson said. ''We're a no-excuse team. We just play. Obviously during the flow of any game, there's a lot of cycles, a lot of highs and lows, and we just have to learn to play through the lows just as much as the highs.''
Tyler Harris had 14 points and made 9 of 12 free throws for Auburn before fouling out. T.J. Lang scored 11.
Shannon Hale added 13 points for Alabama, which made 8 of 30 3-pointers.
Taylor, who had eight points and eight rebounds, got his fifth foul on a 3-point attempt by TJ Lang with 4:49 left. Lang hit all three free throws to bring the lead back to 74-69.
Alabama trimmed the margin to 80-77 when Obasohan made 1 of 2 free throws with 43 seconds left before Bowers and Canty helped ice it from the free throw line.
The Tide didn't make a field goal in the final 3:53 and Auburn's closing field-goal drought lasted even longer. But in a foul-filled game, Auburn made 28 of 40 free throws, attempting 24 and making 15 in the second half.
Canty's hurt ankle didn't hinder him much. He delivered a number of contested 3-pointers, and his first was from several feet beyond the arc.
''Just imagine what he would have done if he wasn't bothered by his ankle,'' Lang said.
Alabama: The Tide made 19 of 28 free throws after going 7-of-20 in a loss to Vanderbilt. ... They have lost four of five games.
Auburn: The Tigers snapped a three-game losing streak in the series. ... Made 11 of 30 3-pointers.
TECHNICALLY SPEAKING: Auburn's Bowers and Alabama's Riley Norris were called for technical fouls after a run-in the first three minutes. It was a physical game throughout, with Auburn called for 24 fouls and Alabama 29.
GAME OF RUNS
Auburn had runs of 10-0, 11-0 and 13-4. Alabama had runs of 12-0 and 9-0. And that was just in the roller-coaster first half, which ended with the Tigers ahead 40-37 after trailing by as many as 10 points.
Alabama hosts LSU on Saturday.
Auburn visits Florida on Saturday.