After resuming on 389-7, Kent pushed their first-innings score to 441, with veteran Darren Stevens the last man out for 136.
Hardus Viljoen then took three wickets as Essex struggled with the bat.
Dan Lawrence made 88, but Essex could only close on 289-9, three short of avoiding the follow-on.
It was a crucial error from 19-year-old Lawrence, who looked set to reach a fifth first-class hundred and guide Essex to probable safety before he aimed for a second successive six off James Tredwell and holed out on the long-on boundary.
He had earlier done well to come through a difficult start - he was dropped at third slip off Stevens on five - to play attractive drives on both sides of the wicket.
But Lawrence received precious little support from a number of Essex batsmen who failed to capitalise on starts - six were out for scores between 21 and 36 on a blameless pitch.
By the end, last-wicket pair David Masters - who was given a guard of honour in his final match before retiring - and Matt Dixon came together with 25 required to avoid the follow-on.
They inched closer and three more runs on Friday will probably ensure Essex draw a match that lost its entire first day to a wet outfield.
Kent continued their dominance of County Championship Division Two champions Essex on day three at Canterbury.