Phil Woodcock’s team – who had qualified by lifting the Northern Counties title at Lindrick – took a 2-1 lead from the morning foursomes and shared the singles for a 5-4 overall triumph.
Hallamshire’s Barclay Brown and Charlie Thornton (Fulford) drew Yorkshire level with a 5&3 win after they had lost the top foursomes.
Hallowes’ Sam Bairstow and Charlie Daughtrey (Rotherham) then returned a two-hole victory to nudge them ahead.
Bairstow and Dan Bradbury, of Wakefield, were beaten in the top two singles, and Daughtrey went down in the penultimate match.
But Brown, Thornton and Howley Hall’s Tom North all won to give the White Rose afternoon parity and an overall triumph.
Brown said: “It’s better winning for a team than for yourself.” He made short work of both his games, and was five under in both his morning and afternoon matches.
Hertfordshire beat Northamptonshire 5.5-3.5 in the day’s other match.
Yorkshire will be up against Northamptonshire on Wednesday and Hertfordshire in their final match on Thursday.