Harvey Hosein hit an unbeaten 66, but four wickets for Joe Denly helped Kent claim victory by six wickets on the final day of the Specsavers County Championship match at The 3aaa County Ground.
Hosein hit his second half-century of the summer, but spinners Denly (4-36) and Adam Riley (4-68) shared eight wickets in the innings to dismiss the hosts for 270, setting Kent 110 to win.
Zak Crawley led the way for the visitors hitting 34 as Kent claim 23 points from the match, while Derbyshire take five.
Four-day cricket is back! Derbyshire host three Specsavers County Championship matches in August and September. Buy your tickets in advance and save.