Jack Carson took three for 87 and Sean Hunt two for 48, but despite a cluster of wickets in the final hour, Sussex were unable to polish off Kent’s tail.
Hastings-born Harry Finch made 115 from 212 balls against his home and former county as Kent closed on 257 for seven, after Sussex had declared on 332 for four, 40 minutes into the morning session.
The visitors began day four on 277 for three, and Matt Quinn, who finished with three for 118, took the only wicket to fall when he had Oliver Carter caught by Marcus O’Riordan for 18.
Travis Head reached 49 not out when the visitors declared, setting Kent a target of 349 to win. The hosts' reply got off to a desperate start when Ollie Robinson had Joe Gordon caught behind for a duck in the first over, but O’Riordan and Finch batted through to lunch, with Kent on 52 for one.
O’Riordan was dropped thrice before he was finally run out in bizarre circumstances for 47. Chasing a single, he nearly ran into his batting partner Finch. As he veered sideways to avoid a collision, the ball was gathered by Tom Haines, who ran him out with a direct hit.
Henio Kuhn faced 27 balls before he was bowled by Carson for four, leaving Kent on 139 for three at tea. Finch reached three figures with a glance off Carson that just eluded leg slip before nestling against the rope, but Kent’s outside hopes of a win dimmed when Dan Lincoln was out for 41, caught by Robinson off Carson.
Conversely, Sussex’s hopes surged when Carson then had Harry Houillon caught by Danial Ibrahim for nine.
Hunt had Finch caught behind and when he subsequently trapped Hamid Qadri lbw for 4 there were still five overs remaining, but Harry Podmore and debutant Bailey Whiteman survived a taught final spell to finish not out on 36 and nought respectively.
The result means Sussex finish bottom of Group C while Kent are fifth, leaving both sides in the third tier when the championship resumes in late August.
Finch said: “I’ve played in quite a few games like this and if you go from the first ball trying to chase it you can end up losing the game, so for us it was taking it each session at a time. I think once we got to tea the wicket started to go up and down, started to spin a bit more. We were just going to play for that first hour and then we did lose a couple of wickets, so that put it (the chase) on hold.
"Obviously you’d love to try and chase that down and win in front of the crowd, but I think we made it a more interesting than we should have done at the end there. I was pretty gutted when I got out because if I think if we’d gotten through those three overs with me and Podders we probably would have just shaken hands.
“I certainly wasn’t expecting (a call-up) when I was playing club cricket (for Hastings Priory) on Saturday. I just played an awful shot, had come off and was quite angry with myself. Then I got a bit of good news. I wasn’t expecting it at all so it was a nice bonus. It’s just nice to take my chance in this game. I wasn’t really thinking about the game (on Saturday night), it was more about getting the paperwork done. I had to rush back to Mum’s get my clothes and sort everything out."
Sussex bowler Robinson said: “I thought it was a good four days for us really, we put out a side, I think the average age was 20, so to do that and almost get the win I thought was a really good effort from everyone involved. (Ali Orr) has really impressed me, he looks like a good all-round player, very solid and he reminds me a little bit of Alastair Cook, he’s very different when he bats and sort of in his own world, his own bubble and nothing really fazes him.
“Jamie Atkins charged in for me this week, he’s got that natural ability to take wickets. He got three in the first spell which got us back in the game really. I never felt like they would get over 300 on that pitch against our attack so we just went with 86, 87 overs really regardless of runs. We got an early one, but it’s a shame we couldn’t have got another."