It was the seventh straight win against SEC opponents for the Flyers (6-2), who improved to 19-8 in the past six seasons against teams from BCS conferences.
Dayton was in control most of the way, although the Crimson Tide came back from a double-digit deficit late in the game to make the score more respectable when Lacey made a 3-pointer as the clock was winding down.
Ahead 3-2, Dayton scored 10 straight points on back-to-back 3-pointers by Benson and Dillard, a fast-break layup by Oliver and a dunk by Benson to jump out to a 13-2 lead at the 15:40 mark.
Behind 20-9, the Crimson Tide went on an 11-2 run to cut the lead to 23-22 on a layup by Randolph with 7:59 left in the half.
Alabama took its first lead of the game, 26-25, when Lacey made two free throws with 5:04 to go. The Flyers then outscored the Tide 13-7 to take a 38-33 lead at intermission.
Dayton maintained its lead throughout the second half. Alabama came within three, 47-44, on a dunk by Lacey at the 16:33 mark, but it was as close as they would get.
The Flyers steadily extended their lead to 70-55, their largest of the game, on a layup by Dillard with 5:38 remaining.
The Tide began chipping away at the lead, but it was too little too late.
The ACC has some pretty daunting venues, from Syracuse's Carrier Dome to North Carolina's Smith Center. Is Duke's Cameron Indoor Stadium the toughest place to get a win?
Four star small forward Chuma Okeke committed to head coach Bruce Pearl and the Auburn Tigers on Sunday over offers from Georgia, Georgia Tech, Florida State, Florida, LSU, Clemson and Mississippi State, among others.
We gave you our rankings of the ACC's toughest venues. Now it's your turn. Which school's venue is the toughest place to play in the ACC?