Having been set 392 for victory in the 91 remaining overs of today's last day, Yorkshire posted century stands for the first and third wickets only to lose their way in the final session and leave Kent to take nine points to their eight.
Needing to average 4.3 runs an over to claim their third consecutive Division One win after successes over Warwickshire and Somerset, Yorkshire got off to a sound start through young left-handed openers Adam Lyth and Joe Sayers.
Lyth got lucky when, on 30, Geraint Jones failed to grasp a tough chance, but he pair kept the scoreboard ticking over steadily at three an over as they put on 155 in 49 overs.
They were both eventually dismissed after lunch in the space of six balls. Lyth, after a fluent 84 from 162 balls, unluckily nicked an attempted leg-glance off off-spinner James Hockley to Jones, who this time made no mistake.
And without addition to the score, the near three-hour stay of Sayers (61) also ended when he followed a turning ball from James Tredwell and steered it to Martin van Jaarsveld at slip.
Yorkshire steadied the ship through former captain Anthony McGrath (55) and Tim Bresnan, who rekindled their slim hopes of victory with a third-wicket stand of 123 in 26 overs.
With 20 overs remaining the Tykes needed a further 151 with eight wickets in hand, a moderate score in Twenty20 terms but a big ask without fielding restrictions and with Kent stationing sweepers back on the boundary ropes.
After reaching a 77-ball 50 with three fours, McGrath holed out to wide long-on off Tredwell before, with three to his name, Jacques Rudolph skied to long-off to give the England off-spinner figures of three for 69.
Yorkshire's final chance rested with Tim Bresnan who looked well set for one last charge having scored 70 from 92 balls.
But, having patted back three successive Tredwell deliveries, Yorkshire captain Andrew Gale called his all-rounder for an ill-judged single to cover and saw him run out to Van Jaarsveld's accurate throw.
Bresnan sloped off and within four overs the sides shook hands on a draw with only six scheduled overs remaining and Yorkshire still 92 short of their target.