Captain Darryl Berry’s side top the table and will secure a fourth consecutive crown if they defeat Cheshire at Royal Liverpool in their final fixture on September 1.
Huddersfield’s Josh Morton delivered the all-important point that hauled them over the finishing line.
Yorkshire boys’ champion Schmidt had partnered Middlesbrough’s James Swash to victory in the morning foursomes, from which the White Rose took an 8-4 lead.
He then showed nerve and skill to win his singles match by one hole in a session that saw the hosts threaten to deny Berry’s men the maximum return from the day.
Yorkshire’s strength in depth, as well as the promise of continued success, was emphasised with recent Yorkshire boys’ captain Matty Raybould also winning both his matches.
Three other players were unbeaten - Malton & Norton’s David Hague, Ben Hutchinson (Howley Hall) and Bailey Gill, of Lindrick - each securing a win and a half.
Table-toppers Yorkshire hold a one-point lead over Lancashire, who yesterday mounted an afternoon comeback to win 9.5-8.5 against Durham at Hesketh. The Red Rose complete their fixtures away at Northumberland.
Yorkshire’s win over Cumbria came just a few days after they secured their place in next month’s English Men’s County Finals in Suffolk with victory in the Northern Counties six-man championship at The Wynyard.