Jamie Milligan’s men hit the front when Rob Apter found the net in the 15th minute.
And it was 2-0 in the 36th minute when Isaac Sinclair was on target, though Lewis Turner halved the deficit on the stroke of half-time for the hosts.
Ewan Bange (68) restored Brig’s two-goal cushion, and Apter added his second – and the visitors’ fourth – in the 76th minute.
James Cadman scored Scarborough’s late consolation goal.
Elsewhere in the division, Brad Gascoigne got the only goal as Lancaster City went down 1-0 at Basford United.
In the National League North, AFC Fylde were 2-0 winners at Bradford (Park Avenue).
Coasters skipper Alex Whitmore scored both goals in the second half.
But there was disappointment for Southport, who lost 1-0 at Brackley Town, Glenn Walker getting the winner in the 20th minute.
Charnock fell at the first hurdle in this season’s FA Vase, losing 5-3 at AFC Liverpool in an all-action first qualifying round tie at Rossett Park.
The hosts went ahead after just four minutes through striker Daniel Cockerline.
Charnock struck back when Jordan Darr turned in a cross from the left from Nathan Nickeas, before Jesse Dowling restored the hosts’ lead.
It was 3-1 on 48 minutes, William McCarthy on target.
Luke Gibson reduced the arrears, but it was 4-2 when Paul Speed rifled home.
Brad Carsley made it 4-3 but as Charnock pressed for an equaliser they were caught out by a sucker-punch as Dowling added the fifth.
Other results – FA Vase first qualifying round: Burscough 2 Hallam 1. NWCL First Division North: Holker Old Boys 3 Garstang 1.