It was the second defeat to the visitors in a matter of weeks for Brig after they were dumped out of the FA Trophy by The North last month.
The home side could not cope with targetman Mark Derbyshire, who scored two and won headers all day.
Brig started the better team and after three minutes Ben Wharton had an effort from range that skimmed the bar.
Trafford opened the scoring when Aaron Burns chested the ball down with his back to goal outside the box, but managed to get to the by-line, where he crossed from the right, and put the ball on a platter for Derbyshire to tap home from a yard out.
And four minutes later, the visitors doubled their lead thanks to a Jonah Gosling header, after more good work from the right, the cross was whipped in and Gosling was at the back post, where his glancing header found the bottom left corner.
The half-time whistle could not come quick enough for Brig, as Trafford went close through Lee Neville’s rasping effort. The second half was unfortunately more of the same, as it took only two minutes for Derbyshire to get his second of the game.
The forward latched on to a long ball and made his way into the box, before his first effort rebounded off the post, but the second bite of the cherry fumbled it’s way in, despite the attempted clearance on the line.
Another 20 scrappy minutes ensued with Brig showing signs of getting back into the match, but, on 72 minutes, Trafford put the game beyond all doubt.
Another long ball made its way to the feet of Mark Derbyshire on the right touchline, but a sublime piece of skill allowed him to cut inside, and his cross-come-shot was deflected into the far corner, possibly off Michael Potts.
With 15 minutes left, Brig attempted to salvage some pride, with Jamie Milligan and Michael Potts coming close near the end, but in truth there was only one team that deserved to win.
The defeat leaves Brig ninth in the table – five points off the playoffs and assistant boss Neil Reynolds said there were likely to be changes for the next game.