The first half saw few clear-cut chances early on, with Harry Scarborough testing goalkeeper Oliver Battersby with an inventive flick only to see it go over the crossbar.
Guiseley then opened the scoring on 34 minutes. Murphy received the ball on the edge of the area, before firing an effort towards goal that took a deflection and flew beyond James Pradic.
It was then 2-0 just two minutes later, Pratt breaking beyond the Brig defence before slotting his effort into the bottom left corner.
The second half was again a story of fleeting opportunities for both sides, although Guiseley were denied a third when Pradic inadvertently used his face to keep out Prince Ekpolo’s close range effort.
Brig then won a string of corners in the closing stages, and one of those almost resulted in a goal when Mark Cullen’s shot went just past the post.
But Brig were unable to find the goal that would have brought them back into the game, with Jamie Milligan’s side next in action against Morpeth Town on September 23.