Kent rallied to close on 375-6, with a lead of 317 runs heading into the final day of the Second XI Friendly at Denby CC.
Chesney Hughes hit 164 on the second day to leave Derbyshire with a first innings lead of 58, but resolute batting from Karim (115) and two further half-centuries guided Kent to a good position.
Beginning their final innings on the morning of Day Three, Kent opener Tom Davis was out to Grant Thornton for four in the sixth over.
This brought Harry Came to the crease to join Karim and the pair set about building a 132-run second-wicket stand.
Came was out to spinner James Sykes for 66, but Karim marched on with wicketkeeper-batsman Adam Rouse to add a further 104 runs in a third-wicket stand which saw Karim reach his century.
Karim was eventually out for 115 and Rouse fell on 66, but 40 from Kashif Ali and an unbeaten 33 from Jordan Cox took Kent to 375-6 at the close, setting up an interesting final day in which Derbyshire will have to dismiss the visitors and then bat well if they are to chase down the Kent total.
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