Nottinghamshire secured a draw on a miraculous final day at Canterbury, at various points of which both sides looked the more fancied for a win.
Kent took two wickets in two balls during the sixth over of the day to leave the visitors still one run behind with just three wickets in hand, having followed-on and been perilously positioned at 78/5 a day prior.
But Joe Clarke, who finished unbeaten on 141 off 277 deliveries, and Brett Hutton, a career-best 84 off 130, combined for a rearguard 37 over partnership worth 148, with the hosts eventually set 161 to win in 32 overs.
The Green and Golds then claimed five wickets within 13 overs as Kent set about an aggressive pursuit of the target, before Joey Evison, Ben Compton and Aron Nijjar shut up shop to leave both sides with a share of the spoils.
The draw keeps all of Kent, Middlesex and Northamptonshire below Nottinghamshire in the Division One table with two games remaining.
Kent took the new ball as soon as it became available after a start delayed by rain, and Micheal Hogan’s fourth delivery got rid of Lyndon James for 39 - ending a stand of 102 - and Calvin Harrison went lbw to the next delivery.
Hutton took a single from the hat-trick ball to bring the scores level and played like he was determined to set Kent a target, advancing to 48 not out at lunch, at which point it was 235 for seven, a lead of 54.
He reached 50 with a single from Nathan Gilchrist and as the game began to drift away from Kent, Clarke drove Hogan for four to reach three figures.
There were few chances but the game sparked to life when Hutton was run out, before Paterson caught by Daniel Bell-Drummond for five with the fourth ball of the evening session and he wrapped up the innings two balls later when Asitha Fernando was caught by Zak Crawley for a duck.
Crawley was sent out to open alongside Tawanda Muyeye but, after crunching Paterson for four, he hit the next delivery straight to James at deep square leg.
Fernando then had Bell-Drummond caught for four by Harrison at slip, Jack Leaning was run out for six and Muyeye tried to hook Fernando and fell to an acrobatic Tom Moores grab.
With Kent reeling on 52/4, Compton was sent out to drop anchor, but Fernando produced a jaffa to send Harry Finch’s off stump flying for seven.
When Joey Evison joined Compton, with a minimum 19.1 overs remaining, they made no attempt to chase the runs.
After an hour’s resistance the latter was caught by Ben Slater off Matt Montgomery, but Nijjar and Evison just about clung to leave Kent with eight points and Nottinghamshire 12.