In their second innings, the defending champions dismissed the hosts for 262, with Dan Worrall taking 4-31 and Cameron Steel 3-38.
After three games, Steel has taken 20 wickets this season, making him the top wicket-taker in the nation.
Matt Parkinson scored his greatest first-class score of 39, and Joey Evison struck 53, but Kent gave in halfway through the afternoon session despite a tenacious rearguard effort that carried them through the morning session.
Ben Compton was caught behind off Worrall in the last over, leaving the hosts 120-5 overnight and 179 runs down. This was a near-fatal blow to their modest aspirations.
Relive the events of the fourth day of the County Championship! Parkinson, who was moved up to the eighth position in the order, had worked hard all winter to strengthen his batting in an attempt to support Kent’s lower order. By lunchtime, though, Kent had reached 203-6, and the seemingly impossible seemed more likely than not.
