They defied the extremely challenging weather to defeat Gloucestershire 6.5-2.5 while in the day’s other match Sussex beat Warwickshire by the same margin.
The results mean Yorkshire will take the title on Thursday if they win or halve against final-day opponents Warwickshire, who have one win from two, as do Sussex.
Wednesday's weather was very challenging with strong winds sweeping across the course to be followed by torrential showers, compete with hail stones on the high ground.
But throughout the golf was of a very high quality, exemplified by Fulford's Jonathan Plaxton, last year's president of the Yorkshire Union of Golf Clubs.
The former England international played through the downpours and was level par for the 11 holes he required to win his singles match 9&7.
It gave Yorkshire momentum after the morning foursomes had been shared.
Garforth's Andy King and Garry Cuthbert (Alwoodley) followed with 5&3 victories and it fell to Ian Clarke, of Lindrick, to ensure overall triumph with a 4&3 win.
Middlesbrough's Peter Ward won on the last hole to improve the scoreline, while Gloucestershire’s Vernon Chappell prevented the singles whitewash with a 3&1 win over Moor Allerton's Johnny Lawrence.
In the foursomes, Plaxton and Clarke had teamed for a 5&3 success, and Lawrence and Halifax Bradley Hall's Andy Whitworth returned a half.
Yorkshire captain Tony Greenhalgh remarked: “We were a bit disappointed not to get two points out of the foursomes, but they came out very well in the afternoon. Whenever we looked at the leaderboards they said up, up, up and that keeps the players going.”