Faced with a target of 309, Derbyshire crumbled for the second time in the match and were bowled out for 117 before tea on the third afternoon with Hannon-Dalby claiming 4-24.
The home side had a chance when they dismissed the Bears for 155 with Michael Cohen taking 5-43 but, chasing 309, a post-lunch collapse condemned them to a fourth defeat of the season.
Warwickshire’s fourth victory takes them to the top of Group One and boosts their chances of qualifying for Division One with two games to play.
Warwickshire skipper Will Rhodes felt his side’s first innings score of 270 in testing conditions was the key to the victory.
“It was a tricky pitch and when we got inserted we didn’t know how the game was going to play out so to get 270 has won us the game,” said Rhodes.
“We knew on that wicket our attack would bowl any team out twice so we just needed to get enough runs and give ourselves a chance. To play the way we did and with the ball we were fantastic so it’s a pretty perfect result really.”