Having edged the morning foursomes 3.5-2.5, captain Darryl Berry’s side shared the honours in the 12 singles to ensure overall victory.
Shipley’s William Whiteoak won the top match, but the next five matches only returned half a point between them and that came via a superb fightback from Bawtry’s Ben Brewster, who was dormie three down but halved.
Steve Robins carried the weight of playing on his home course well to gain a two-hole lead by the 15th in the second match out, but unfortunately his opponent battled back to take the three closing holes and with it the full point.
Jack Lampkin, of Ilkley, added a second point to the one he had annexed in harness with Jamie Harrison (Rotherham) and that left the latter, in the final match, with a chance to seal victory.
He needed a half on the 18th to give Yorkshire a 9.5-8.5 overall triumph and did so, despite being unable to get up and down from beside the green.
Luke Robinson (Oakdale) was the third member of the side to win both his matches.
“This was a big win for us,” said Berry, whose side had shown similarly doughty character in earning a 9-9 draw with champions Lancashire in their opening match.
“We have three remaining matches and the aim is to win them all as big as we can.
“Conditions were really tough on Saturday, really windy, and the Hull greenkeeping staff had done a fantastic job.
“They got the course as good as they possibly could, it was excellent, and they were sensible with their pin positions, given that some of the gusts were around 40mph.”
Next up for Yorkshire are Cheshire at Ilkley on July 11.
Yorkshire now lie second in the league behind Cheshire, who beat Northumberland 15-3 on Saturday.