Darryl Berry’s team built a platform for success with a 3-0 clean sweep in the morning foursomes at the Midlands venue.
Hull’s Steve Robins and Yorkshire champion Ben Hutchinson (Howley Hall) then got them over the winning line with singles victories.
Robins won five holes in a row from the eighth – with the help of three birdies – before closing out his game on the 15th.
Hutchinson was three under and five up at the turn, and although he did not putt as well on the back nine, he won 3&2
“It was the winning point and that’s what counts,” he said.
Warwickshire’s Patrick Ruff, who was two down at the halfway point, took English amateur champion Dan Brown (Masham) to the 18th and their game was halved.
Shipley’s Will Whiteoak also returned a half and Wheatley’s Kealan Lowe, the new Yorkshire Order of Merit champion, won the last game 2&1.
Yorkshire captain Berry said: “It’s been a very good day’s work. I’m happy with the way they played and it’s a deserved win.
"They have stuck to what they had to do and their attitude has been brilliant. They’re all up for it.”
On Saturday Hampshire, 5-4 winners over Cornwall on day one, play Warwickshire while Yorkshire take on Cornwall.
The last time Hampshire won the championship was in 1996 when Olympic champion Justin Rose - who has sent them a good-luck message this week - was in the team.