Former Scarborough Athletic and Whitby Town man Beadle tapped in from close range to hand Edgehill a 1-0 lead heading into the break.
The visitors dominated the second half and it was soon 2-0, Stubbings cutting in off the left flank before firing in at the near post.
It was soon 3-0, sub Robbie Scarborough scoring within three minutes of being introduced via a neat finish.
Beadle and Stubbings both hit their second goals to make it 5-0 before Jackson Jowett wrapped up the scoring with the goal of the game, lobbing the keeper from 40 yards out.
Boss Steve Clegg handed the man of the match honours to midfielder Jamie Patterson, with skipper Joe Gallagher also standing out.
Benji Harrison was Seamer's man of the match.
Champions and league leader West Pier picked up a comfortable 7-1 win at Sherburn to maintain their challenge.
Sean Exley bagged two goals within 30 minutes to set Pier on their way, with Neil Thomas' close-range finish handing them a 3-0 advantage at the interval.
An outrageous 45-yard half-volley from Martin Cooper then left the Sherburn keeper with no chance as the ball flew in off the underside of the bar to hand Pier a 4-0 lead and put the result beyond any doubt.
Pier's fifth came via Exley's third goal, Rich Barker then hitting a sixth for Andy Spivey's side.
Nick Ellis scored for Sherburn, but Pier had the last word as Rich Tolliday tapped in to wrap things up at 7-1.
Cooper was Pier's star man, with midfielders Sam Garnett and Will Jenkinson and hat-trick hero Exley also impressing.
Newlands Park and Itis Itis Rovers shared the spoils after a thrilling 4-4 draw.
Martin Cappleman's Park side led on four occasions, but were pegged back each time by visitors Rovers.
Newlands' goals came via doubles from Ben Luntley and Tom Scales, while Ryan Matson hit a brace for Rovers, with a Jack Ramos strike and an unfortunate Kile Fields own goal sealing their point.
Park gloveman Craig Thordarson was the hosts' man of the match, while Sean Bloom was Rovers' star man.
Hunmanby United thumped rock-bottom Goal Sports 16-1.
Man of the match Ryan Baldry led the United charge with four goals, while Ben Briggs, Tommy Wilson and James Pinder all hit hat-tricks.
United's other goals came courtesy of Luke Kirby, Andy Wardell and John Emmerson.
Goal Sports' goal came from Josh Christlow.
United boss Leigh Franks paid tribute to hosts Goal Sports for battling on despite the heavy defeat.
Scalby failed to raise a side for their game at Filey Town.
Filey Town P-P Scalby, Goal Sports 1-16 Hunmanby Utd, Newlands 4-4 Itis Itis Rovers, Seamer 0-6 Edgehill, Sherburn 1-7 West Pier