Daniel Wasteney, Joe Dean and Jonathan Thomson all won in their match against Durham at Eaglescliffe.
Wasteney won by 4&3, Dean 2up and Thomson by 3&2 in a 13-5 Yorkshire win.
Only two points separated the teams after the foursomes, but Yorkshire managed to find another gear after lunch and won seven of the afternoon singles, halving the other two.
Both Lancashire and Yorkshire have one hundred per cent records, and sit comfortably at the head of the English Golf Union competition table.
In the next round of matches, Yorkshire take on old rivals Lancashire in an away Roses Match at Pleasington Golf Club, Blackburn on the 13th July.