Kent 176 for 6 (Stevens 59) beat Yorkshire 175 for 9 (Coles 6-32) by four wickets
Matt Coles continued his devastating form against Yorkshire this season by taking 6 for 32 to put Kent on course for a four-wicket victory at Headingley.
The 22-year allrounder, who has been included in the England Lions squad for the match against West Indies, scored his maiden century in the opening Championship fixture on the ground and in the return clash at Canterbury he claimed four wickets in Yorkshire's only innings.
Coles picked up his scalps in two bursts, which restricted Yorkshire to 175 for 9, and although Kent had only four balls to spare at the end, they were never put under any undue pressure.
Sam Billings and Rob Key made a sound start to the Kent reply with a 57 stand in 13 overs, before Azeem Rafiq struck three times, but Darren Stevens snuffed out any real chance of a Yorkshire fightback. Brendan Nash played his part too, but when the stand was worth 65 in 12 overs, offspinner Joe Root started a new spell and Stevens drove his first ball to Gary Ballance at long-on.
With the game almost won, Sam Northeast was lbw to Moin Ashraf and the scores were level in the penultimate over when Root sent back Nash, leaving Jones to make the winning run.
Yorkshire never fully regained their poise after making a nightmare start to their innings which saw them reduced to 22 for 4 in six overs. Joe Sayers attempted to drive Mark Davies but only succeeded in edging to slip and Coles set out on his destructive trail by comprehensively bowling Phil Jaques before he had scored.
Jonny Bairstow presented Coles with a return catch and the bowler followed up by pinning Ballance lbw first ball to give him three wickets for 11 runs off his first three overs.
Yorkshire captain Andrew Gale had combined with Root in an attempt to repair the damage, Gale lofting Stevens for four with a straight drive and then just clearing Billings on the midwicket boundary with a sweetly struck six.
The fifth wicket pair had added 70 in 19 overs when Gale was given out lbw for 44 to Stevens off a ball which may have found the inside edge first. Adil Rashid got moving with some delicate late cuts and Root continued to bat with calm authority until he squirted a drive at Adam Ball straight into the hands of Northeast at backward point.
Coles returned to dismiss Rafiq, Steve Patterson and Rashid and as Yorkshire's limped to an under-par total.