Second in the Championship table before this game, they put themselves in line for another 11 points at least, in the welcome Kent sunshine, despite a wonderful 161 in adversity by Trevor Ward. By the close on what was effectively the second day of a three-day game, the visitors had extended their lead to 80.
Matthew Fleming's brilliant one-handed catch to see off Michael Vaughan prevented them establishing an even better platform and, with a benign wicket showing no sign of deteriorating, they may be unable to force the victory that could propel them to the top of the table.
More play had been possible during the first two days than at any other ground - 105 overs - but Yorkshire batted on in the morning to secure a fourth batting point, which came after 30 runs had been added, most of them by Alex Wharf, a 20-year-old from Bradford, standing in for Darren Gough.
Wharf, who made his debut in 1994 but was not called upon at all last season, contributed 41 to the eighth-wicket stand of 54 with Richard Blakey before losing his off-stump to Martin McCague. Blakey was left unbeaten on 60, his highest Championship score for two years.
Kent were not to be rushed. David Fulton saw out 28 deliveries before taking a run; Fleming had faced the same number for 17 and was just opening up when he top-edged Peter Hartley high in the air. Alex Morris beat the wicketkeeper Blakey to take the catch comfortably.
Back to the pavilion and another cigarette for Fleming, doubtless wondering how much longer he will open the innings. He has reached 20 only once in six Championship knocks and with Mark Benson submitting to the surgeon's knife last week, Neil Taylor's supporters around the ground believe it is high time he returned from the cold.
Fulton has been more successful. He forced Hartley to take a rest with two hefty pulls but then played back to Chris Silverwood and was leg before for 34. In his next over, Silverwood, another promising youngster, got the best notch yet on his barrel by having Carl Hooper caught at slip second ball.
Graham Cowdrey took almost as long as Fulton to get off the mark, before slashing past gully. Swishing and missing much of the time, he made seven in a stand of 50 with Ward before trying to sweep Richard Stemp's left- arm spin and giving David Byas a second catch.
The skipper held a third one to see off Nigel Llong in Alex Morris's second over and Craig White returned to bowl Steve Marsh. Fortunately for the home side, Ward was imperious. Briefly nervous in the nineties, he reasserted himself after tea, rushing from 100 to 150 in 43 balls, nine of them struck to the rope.
Apart from Dr Julian Thompson, with a lusty 28, there was no other support for Ward and after he lost his off-stump to White, the innings collapsed. The last four wickets went for 16, three of them to White at no personal cost.
Min Patel, page 27