Alan Richardson claimed three for nine with the new ball as Kent took lunch at 68 for five. Sam Northeast, with 42 not out, did the bulk of the scoring.
On day three at the County Ground, Northamptonshire took four wickets in the first session to leave Leicestershire 134 for five.
Australian seamer Trent Copeland took three of them, including Ramnaresh Sarwan just before lunch.The Foxes will restart 221 behind.
Essex were making steady progress in their match against Glamorgan at the SWALEC Stadium.
They added just one run to be bowled out for 345 - Michael Hogan taking the final wicket to close with six for 70 - but then left Glamorgan 80 for three.
David Masters took two of them to add to his first-innings five-wicket haul, with Ravi Bopara chipping in with the third.
With seven wickets left in hand, Glamorgan remain 34 adrift.
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