The White Rose side required only a half from the match to claim the title and won the morning foursomes 2-1 against Warwickshire.
However, through the afternoon, as fortunes swayed one way and then the other, the title looked anything but assured.
But captain Tony Greenhalgh’s side claimed critical points on the 17th and 18th greens in the final matches and emerged the 5-4 winners.
Greenhalgh commented: “We are absolutely ecstatic. It’s the first time we have won this trophy and so it’s very special.”
He was standing in this week for regular captain, John Grimbleby, who was unable to lead the team because of family commitments.
“I feel a bit of a fraud because John has captained the team all year,” said Greenhalgh. “But we’re delighted to bring it home for him.”
At the start of Thursday’s matches Yorkshire were in pole position, having already beaten Sussex and Gloucestershire.
They knew only a defeat could possibly deny them the title by triggering a countback and bringing Warwickshire and Sussex into the reckoning.
Yorkshire’s 2-1 lead after the foursomes came courtesy of some gritty play from Alwoodley’s Garry Cuthbert and Peter Ward, of Middlesbrough, who won despite being one down after 15.
As the singles unfolded, Warwickshire took charge and, with six holes played, they trailed in only one game. Andrew Carman kept the momentum going as he eased to a 6&5 win and Tony Allen edged the team ahead when he won on the 17th.
The tension mounted as the final games played out the closing holes. Moor Allerton’s Johnny Lawrence, who was ahead throughout his game, added his point on the 17th.
Garforth’s Andy King had to wait until the 17th before getting ahead in his game, but then held on to claim a one-upwin. But Warwickshire’s Peter Gordon kept the team tally level when he won by the same margin.
The decider was the last game on the course and Ward and Warwickshire’s Rob Soen were all square as they stood on the 18th tee.
Soen hit a superb approach into the green, which finished about three feet from the hole, but Ward did even better, playing his to within six inches of the cup. It proved decisive when Soen’s birdie attempt slipped past, putting the title securely in Yorkshire’s grasp.
“It was a very demanding afternoon,” said Greenhalgh. “I kept looking at the scoreboard and Warwickshire were comfortably ahead. But Johnny Lawrence, Andy King and Peter Ward brought in the points when we needed them.”
Sussex wanted a big win to support their challenge in the event of a countback. But Gloucestershire ended their title hopes when they held them to a draw, posting their first point on the leaderboard.
“It’s Gloucestershire grit,” joked team captain Rob Stephens after his players found a supreme touch on the 18th green.
First Carl Gyde holed from about 50ft for a winning birdie to finish two up, then Mike Parkin slotted a 20-footer to halve as the team worked their way to the 4.5-4.5 score, with four of the six singles finishing on the 18th.
“It was a great match and we owed it to the other teams to be as competitive as we could,” added Stephens.
Sussex finished the championship as runners-up, followed by Warwickshire and then Gloucestershire.