Kent 394 (Denly 87, Finch 85, Critchley 5-88) trail Essex 591 for 7 dec (Cox 207, Snater 83*, Pepper 82, Elgar 77, Browne 65) by 197 runs
Kent fought back on day three of their Vitality County Championship derby with Essex on Canterbury, surviving till the final over of the day before they were after being bowled out for 349 in the final over.
Joe Denly hit 87 and Harry Finch 85 to boost the hosts' chances of batting out a draw after they were dominated on the first two days.
Matt Critchley took five for 88, but Essex laboured without Sam Cook, who'd pulled up injured on day two.
The hosts' morale had taken a battering on day two and they'd closed on 118 for four, still 473 in arrears, but they weren't about to surrender without a fight.
Conditions were blustery and overcast at 11 am but the forecast rain failed to materialise and Denly and nightwatcher Matt Parkinson batted through the entire morning session.
There were occasional alarms, such as when Dean Elgar couldn't cling on to a violently drive from Parkinson when he was on 31, but the spinner passed his previous first-class best of 39 with a single off Harmer and had made it to 45 at lunch, at which point Kent were 203 for four.
Denly then drove Snater for four to bring up his fifty, but Parkinson was denied a maiden red-ball 50 when Jamie Porter trapped him lbw.
Finch was on four when he pulled Beard to the boundary, but Critchley couldn't pull off a tumbling catch and the drop proved expensive.
The only other wicket to fall in the session came when Denly, who looked destined for a century, misjudged a Critchley delivery and was caught by Aaron Beard at long on.
Successive byes from Critchley allowed Kent to get a third bonus point with four balls to spare in the 110th over and it was 302 for six at tea.
Finch glanced Beard for four to bring up his half-century and as the evening session dragged on Essex's increasing frustration started to show with an embarrassing appeal for a catch against Joey Evison from a ball that had clearly been driven into the ground.
They finally broke through when Evison tried to sweep Tom Westley and was bowled for 29. Westley then had Finch lbw and with Wes Agar hurt after injuring his shoulder on day one Arafat Bhuiyan was sent out with Kent still 78 runs short of the follow on target and six overs remaining.
Grant Stewart played conservatively by his standards, but still managed to dump Westley for six over cow corner, only for Critchley to bowl Bhuiyan at 5.45pm, with two scheduled overs remaining.
Agar duly walked out needing to survive for three minutes to spare Kent an awkward over following on and he duly blocked out five balls to at least spare the hosts the dilemma of weather or not to send in a nightwatcher to open.
With the field in, Stewart then blasted Harmer for six in the day's penultimate over, but Critchley pinned Agar lbw with the first ball of the last over, to set up a potentially fascinating final day.