Football: Rangers boss slams his side's Blyth spirit
But injuries to defender Richard Vauls and striker Nick Wellecomme, together with a red card for midfielder Levi Reid, did the visitors few favours in the North East.
Reid's second booking 10 minutes from time was sandwiched between Brayson's goals, but Stafford boss Chris Brindley was frustrated by the attitude of a number of his players.
He said: "It was a disappointing way to go out. We huffed and puffed a little bit, but two or three players weren't at the races really and the game passed them by. We were a bit lightweight.
"We didn't force it enough early on when we had the elements with us. It was an average game to watch between two sides short on confidence."
Stafford's best chance of the opening half came early on, midfielder Tom Thorley firing just wide of the Blyth goal.
The home side went closer still to breaking the deadlock when John Alexander's effort crashed against the Rangers' upright.
The striker then had another effort into the side netting before Brayson handed Blyth a 69th-minute lead with a shot from the edge of the Rangers area.
Reid saw red on 80 minutes and the match was finally put beyond Stafford's reach four minutes later, when Brayson bagged his second after a through ball sliced the Stafford defence in two.
There was almost a third for the home side in injury time when a Gareth Williams free-kick beat keeper Lee Evans, only to rebound off the Rangers crossbar.
Brindley said: "It's a blow that we have not had any prize money from the two FA competitions this year, but ultimately we have to remain in this league."
Stafford Rangers: Evans, Wooliscroft, Vauls (Patrick 32), Thorley, Wilson, Johnson, Reid, Moult, Wellecomme (Samba 71), Kasiama (E Francis 68), A Francis. Unused: Rogers, Whitehouse.
Comment on this story