Kent 561 (Denly 106, Crawley 96, Stewart 85, Henry 81, Palladino 5-113) and 110 for 4 beat Derbyshire 400 (Madsen 93, Godleman 71, Hughes 66) and 270 (Hosein 66*, Denly 4-36, Riley 4-68) by six wickets
Joe Denly made a late entrance to record his best first-class figures as Kent moved into the promotion places with a six wicket win over Derbyshire in the Division Two match at Derby.
Denly was of the field for most of the final morning through illness but took the last four wickets to finish with 4 for 36 to bowl Derbyshire out for 270 with Harvey Hosein top-scoring with an unbeaten 66.
That left Kent with a target of 110 and although they lost wickets with the finish in sight, a 23-point victory took them above Sussex into second place.
Derbyshire began the day 78 runs behind and Matt Henry struck early by finding just enough away movement to have Alex Hughes caught behind and become the second bowler to take 50 Championship wickets this season.
Tom Lace had shown good technique and temperament in both innings on his first-class debut and was looking secure until a change of bowling gave Kent another success.
Grant Stewart's second ball beat Lace's forward push and took the top of off stump to dismiss the 20-year-old for 43.
Kent struck again in the next over when Matt Critchley edged Adam Riley and the ball stuck between the knees of Billings as he dived forward.
Sean Ervine drove Stewart through the covers for four but became another victim for Riley in the 53rd over when the ball hit the back of his bat via pad and looped to silly point.
At 137 for 6, an early finish beckoned but Hosein and Hardus Viljoen took the game into the afternoon and ensured Kent would have to bat again.
The pair survived for another eight overs after the interval until Viljoen sliced Denly to point but Palladino joined Hosein to force Billings to take the second new ball.
Kent's frustration increased when Riley put down a head high chance to gully with Hosein on 44 and he reached his 50 in the same over by driving Stewart for his seventh four.
Denly broke the stand when Palladino was lbw to one that kept low two overs before tea and the leg-spinner quickly wrapped up the innings after the interval leaving Kent 28 overs to knock off the runs.
Sean Dickson showed his dismay at being given out caught behind off Lockie Ferguson in the fifth over but Zak Crawley and Heino Kuhn added 57 in six overs before Crawley edged Hamidullah Qadri to slip.
Kuhn sliced Critchley to point and Denly gave Qadri a return catch but Kent survived the late drama to secure a fourth away win.