Matthews dropped a shot at the second hole, but played flawlessly for the remainder of the round, carding six birdies for his five-under-par 66.
He finished a shot clear of Bradley Park’s Richard Law and Yorkshire amateur champion Ben Hutchinson (Howley Hall).
Also one step from the Open Championship, which will be staged at Royal Birkdale from July 19-23, are Lindrick’s Luke Jackson, who carded a 69, and unattached professional Jeremy Kavanagh, who was another shot back.
Law was level par at the turn, having immediately surrendered the shot gained at the third hole with a bogey at four. But he began the back nine in superb fashion with an eagle three and followed that with birdies at 12 and 15.
Hutchinson got off to a faltering start with a dropped shot at the first, but retrieved it at the third.
He then produced a scintillating spell either side of the turn, birdieing four holes in six from the seventh, and added another at the 18th.
Like Hutchinson, Jackson was one over after the first, but followed with 14 pars and birdies at the third, seventh and 13th.
Among those just outside the qualifying places were former Yorkshire champion Julian Taylor (Marc Oliver Bathrooms) and Huddersfield amateur Josh Morton, both on 71.
Taylor had five birdies that were offset by the same number of bogeys while Morton had four of each.
Amateurs Bailey Gill (Lindrick) and Scott MacGregor (Wakefield) both carded one-over-par 72.
There were 12 other regional qualifying stages, several involving Yorkshire players, and scores included the following:
Burhill New Course: 79 – Barclay Brown (Hallamshire).
Fairhaven : 76 – Simon Coumbe (Pontefract & District); 88 – Robert Wragg (Hallowes).
Frilford Heath: 76 – David Houlding (Moortown).
Little Aston: 76 – Alex Fitzpatrick (Hallamshire); 77 – Alexander Ball (Beauchief).
Luffenham Heath: 72 – Ben Brewster (Wheatley); 74 – Neil Kinghorn (Wakefield); 80 – Jamie Shepherd (Hallamshire).
Northumberland: 74 – James Cass (Fulford), Elliott Butterworth (Middlesbrough), Martin Brown (Pike Hills); 75 – Bradley Rowntree (Richmond); 76 – Andrew Richardson (Middlesbrough); 77 – Stephen Pullan (Sand Moor); 82 – Glen Ient (Catterick).
West Lancs: 75 – Rob Booth (Crosland Heath).
Final qualifying will be held over five courses next Tuesday – Gailes Links, Notts Hollinwell, Hillside, Royal Cinque Ports and Woburn – with a total of 15 places available to a field of 360.