Joe Denly hit his third century of the campaign for Kent, before Derbyshire battled back in the final session of the opening day at The 3aaa County Ground.
Denly top scored with 106, while Zak Crawley (96) and Heino Kuhn (51) both hit half-centuries. Derbyshire responded in the last session of the day, but Kent closed the day in a good position on 365-6.
Tony Palladino (2-63) and Hardus Viljoen (2-68) both took two wickets apiece for the hosts.
After losing the toss and asked to bowl first, Derbyshire made the perfect start courtesy of Viljoen as the tall fast bowler had opener Sean Dickson lbw for four in the third over of the day.
But it would be the only success of the morning session as Denly and Crawley took the attack to the Derbyshire bowlers on a good batting track, moving the score to 133-1 at lunch.
The visitors continued to score well in the afternoon session before Crawley fell just short of a maiden first-class century when he was lbw to Palladino. The opener hit 11 fours and three sixes in his career-best knock of 96.
It was again the only wicket to fall in the session, with Kent 259-2 at tea. Derbyshire would, however, enjoy an improved final session taking four wickets.
Palladino removed Kuhn shortly after passing his half-century, before Viljoen finally dismissed Denly, who faced 215 balls for his 106 which included 12 fours.
Alex Hughes (1-34) and Lockie Ferguson (1-66) then both picked up a wicket each in the closing stages of the day, with Daniel Bell-Drummond and Grant Steward the not out batsman for Kent.
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