Both sides have two wins from as many matches after Yorkshire defeated Cornwall 5.5-3.5 and Hampshire bested Warwickshire 6.5-2.5 on Saturday in strong winds.
Following Yorkshire's first-day 7-2 defeat of Warwickshire, when Hampshire edged Cornwall 5-4, captain Darryl Berry's side have a one-point game advantage over Sunday's opponents.
It means that a tied contest between them will be enough for Yorkshire to lift the title for the first time since 2007, but they are certain to target a clean sweep on the third and final day.
Berry's men had won the foursomes 3-0 against Warwickshire, but trailed 2-1 against Cornwall, Dan Brown (Masham) and Hull's Steve Robins their only winners, making it two from two for them as a pairing.
New Yorkshire champion Ben Hutchinson (Howley Hall) was beaten in the top afternoon singles, but Shipley's Will Whiteoak had already stormed to a 6&5 win, executing Berry's game plan.
“I want the first point on the board to be a Yorkshire point to level the game," Berry had urged his men at lunch-time.
Whiteoak was bogey free and three under par when he won. “We needed a couple of players to get some early points and hopefully it would seep back to the bottom end,” he said.
Robins then extended his perfect record to four wins in four matches so far by winning his afternoon singles contest 4&3.
He was also bogey free and was four under when he claimed the team’s second point.
English men's champion Brown halved for a second consecutive singles session, but Yorkshire match play champion Bailey Gill (LIndrick) and Yorkshire Order of Merit winner Kealan Lowe (Wheatley) both won, 3&1 and 4&2 respectively, to secure the White Rose's overall triumph.
Lowe showed tremendous class as he closed out his win, playing a remarkable shot out of thick rough behind the 15th green, putting the ball inches from the hole. He then slotted a tricky, downhill birdie putt on the 16th for the win.
Gill had been three down after six holes, but turned the match around with three consecutive birdies from the 10th, which got him to one up, and, as the match moved towards the closing holes, he played crucial shots close to the pin.
Brown had holed a 25ft birdie putt on the 17th green to go down the last one up, but his opponent Rob McGregor replied by holing a 35-footer on the 18th for birdie and a half point.
Berry commented on his team’s performance: “It was all about getting the momentum to feed the team and the guys have done what they needed to.”