During an entertaining shortened final day, Gary Ballance fell four runs short of a 41st career century and a first since July 2019 following illness and injury.
A wet outfield delayed day four until 2.45pm - a knock-on effect of the day three washout - and both sides secured useful bonus points.
Yorkshire, who remain second in the table, resumed their first innings on 240 for five from 77 overs in reply to 305 and ended 321 all out inside 106 thanks to Ben Coad’s unbeaten 33 off as many balls at number 10.
Yorkshire have now won three and drawn two and claimed 13 points, while Kent secured 14 but remain bottom with two draws and three defeats.
What is expected to be the final day of cricket without a Headingley crowd was delayed due to a damp Emerald Stand end of the ground.Yorkshire were aiming for as many as 160 runs in 33 overs for five batting points, with Kent requiring four wickets for three bowling points.
Ballance resumed on 91 and was one of three wickets to fall before tea - 269 for eight in the 97th over.
Ballance pulled Darren Stevens for four to move to 96, only to fall run out by a direct hit from Marcus O’Riordan at the striker’s end after Dom Bess had pushed the ball to backward point.
It seemed as if it was Ballance’s decision to run.
Play was taking place under floodlights, and the early setback of losing Ballance and Bess - bowled by Stevens to leave the score at 256 for seven - limited their run-scoring expectations.
Jordan Thompson and Steve Patterson attempted to up the ante, only for the latter to be caught behind cutting at seamer Gilchrist at the start of the afternoon’s final over.
Coad came to the crease immediately after tea and dominated a 35-run stand for the ninth wicket with Thompson, hitting four of his first 12 balls to the boundary.
A brief delay for bad light at 5pm was initially interpreted as the end of the fixture by onlookers, only for play to resume 10 minutes later with Yorkshire 304 for nine in the 104th over.
But Duanne Olivier holed out to long-on off Jack Leaning shortly afterwards to bring things to a close.
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