Derbyshire resumed on 112-6 and lost their last four wickets in just 8.2 overs as they were dismissed for 128.
Dillon Pennington completed the first five wicket haul of his career and finished with figures of 14-4-32-5.
Derbyshire remain rock bottom after a third heavy setback in the last four matches, a 310 run setback and two innings defeats.
They paid the penalty for dropped catches on the opening day, including Jack Haynes who went onto make 97.
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Their young and promising bowling attack bowled too many ‘four’ balls while the batting, with the exception of Matt Critchley and Wayne Madsen, crumbled.
Derbyshire CCC Head Coach David Houghton said: “Our problem at the moment is pretty plain to see. We haven’t batted well as a unit yet.
“The only game where we’ve been on the front foot was the home game against Worcestershire where we scored 400 batting first.
“If you play every game from a position of scoring 400 in your first innings, then you are going to be able to play a different brand of cricket.
“If we are batting second we are only getting 180-200 and if we batting first we are getting bowled out too cheaply.”
Club Captain Joe Leach picked up the prized wicket of Madsen who had resumed on 43.
He had looked set to complete his 11th 50 plus score in 19 innings against Worcestershire.
But Madsen added only two more before edging a fine delivery and was caught by keeper Ben Cox.
Dillon Pennington opened the attack from the New Road End and in the next over he accounted for new batsman Ben Aitchison before he had scored.
Pennington found the thinnest of edges but it was sufficient to provide Cox with another straightforward catch.
The game quickly came to a conclusion with Sam Conners (0) playing onto Pennington and Dustin Melton (1) edging Alzarri Joseph to Daryl Mitchell at slip.