James Tredwell and Calum Haggett ripped through Derbyshire on the final morning at Derby to leave Kent chasing 175 for victory.
They took four wickets each as Derbyshire lost seven for 45 in 93 balls to collapse to 94 all out and by lunch, Kent had reached 26 without loss from six overs.
Although the murkey conditions were good for bowling, Derbyshire batted poorly with at least three batsmen misjudging the length as Haggett claimed career-best figures of 4 for 15 in 6.4 overs.
Tredwell bowled unchanged through the innings from the Racecourse End and started the slide when Neil Broom was superbly caught by Adam Ball at first slip for 18.
After Haggett trapped Wayne Madsen lbw for 37, the innings fell away with Tredwell bowling first innings centurion Shiv Thakor to finish with 4 for 45 in 14 overs.