The fourth-wicket pair of Daniel Bell-Drummond and nightwatchman Fred Klaassen batted through the morning session on day four to briefly raise hopes of an improbable draw.
For Yorkshire, it was all fairly straightforward in the end.
Kent slipped from 84-3 once that stand was broken by the seventh ball after lunch to 211 all-out, losing by 172 runs at 5.15pm with 15.1 overs left in the match.
Yorkshire’s second win in three Championship games this season, to go with one draw, was set up by a second innings hundred from Gary Ballance, which helped overturn a first innings deficit of 86 runs, and sealed by a patient and persevering bowling display.
An attack led by Duanne Olivier and Ben Coad, the latter starring with 6-52, was always likely to be too strong for opponents who may face a battle to stay in Division One along with fellow promoted club Warwickshire.
Coad was his usual magnificent self, while Olivier scared the living daylights out of the batsmen at times, striking a couple of them on the helmet to lift the number of concussions checks he has forced this season to nine.
The South African pace bowler seems to positively enjoy hitting people on the head almost as much as he enjoys taking wickets, he chipped in here with five wickets in the match.
Clanging players on the helmet, of course, is no laughing matter, but Olivier’s pace has an unsettling effect.
It was enough to see off Kent opener Sean Dickson on the third evening as he fended tamely to short leg, the visitors tumbling to 34-3 in an eight-over spell in the run-up to stumps, a position from which they never recovered. Not that Olivier, Coad and co had it all their own way.
The only man nursing a sore head yesterday morning was Yorkshire captain Steve Patterson as he strived to work out how to separate Kent’s fourth-wicket pair.
It might have happened just 20 minutes in, but Adam Lyth dropped Bell-Drummond at second slip off Olivier in the mostly gloomy, overcast conditions.
Later in the session, Lyth’s reaction suggested that he also spilled Bell-Drummond at slip off spinner Dom Bess, the hosts going into lunch on 84-3, having added 50 in the session in 32 overs.
Lyth’s slip catching is normally sound, and the opening batsman proved it by holding two chances in the space of nine balls just after the break.
Olivier found Klaassen’s edge to end an innings of 13 from 110 deliveries in 143 minutes, Lyth taking the ball in the midriff area, and then Coad removed Heino Kuhn for a duck, Lyth this time tumbling low to his left.
With Tim Bresnan having to leave the field in the morning due to a suspected calf tear, having slipped over as he prepared to deliver his first ball, Yorkshire were a bowler down as they sought to apply the coup de grace.
Bresnan will have a scan on an injury which, in a worst-case scenario, could rule him out for up to six weeks.
Patterson made a key contribution when he had Bell-Drummond lbw for 41, the batsman playing all around a delivery that ended his three-hour vigil.
Ollie Robinson, the first innings centurion, played well for 35 having been struck on the helmet by Olivier when he had 11.
But he was outfoxed by a slower delivery from Coad, which he spooned up to Gary Ballance in the covers, leaving Kent in the mire at 142-7.
The sun now made a fleeting appearance, a welcome guest for the few hundred spectators, and it remained, for Yorkshire, a game of patience.
The eighth-wicket pair of Alex Blake and Harry Podmore survived for 22 overs, Jack Leaning’s off-spin removing Blake lbw just before the second new ball.
Then, as the skies turned overcast again, it was over to Coad to finish things off.
He bowled Harry Podmore for 29 to claim his fifth wicket and then had Mitch Claydon caught at short-leg to cap suitable celebrations.
Patterson said: “It was a tough game this week, and we’ve had to really work hard and earn the right to win. From being 90 odd for six on the first morning and 120 for seven, to somehow put ourselves in a position to win by nearly 200 runs is a testament to the lads’ work over the four days.
“We toiled very hard for three-and-a-half days and we’ve got our rewards. After those first couple sessions, we picked it up and I’d say we were on top after that.
“If you’re going to win a game like that, you need more than one person to chip in.
“Gary Ballance’s hundred was outstanding and Coady’s six-for today, but everybody made their own contributions and pushed us towards getting there in the end,” he added.
Yorkshire have allowed pace bowlers Jared Warner and Josh Shaw to go on a month’s loan.
Warner has joined Sussex and Shaw has rejoined Gloucestershire.
Warner, 22, who made his first team debut in the Royal London Cup earlier this month, said: “I want to do well and prove a point to Yorkshire and long-term get some consistency into my game.
“Short-term, I want to contribute to Sussex who have shown faith in signing me and help them to some wins.”
Shaw, 23, is returning to Bristol for his fourth spell.
“Gloucestershire are a club I know well and the last three times I’ve really enjoyed myself,” he said.