Goals from Ntumba Massanka and Callum Harris were enough for the visitors, who ended their three-game winless run in the process.
The match started at a fast pace, with both sides having early chances.
Brig goalkeeper Mateusz Hewelt, who signed for League Two side Tranmere Rovers earlier in the week, was forced into action to parry behind Massanka’s well-struck effort from range.
At the other end, on 10 minutes, Matthew Thomson then had a shot deflected for Brig.
A minute later, Stalybridge took the lead. Justin Johnson surged down the left flank before squaring the ball to Massanka, who made no mistake with his first-time effort in putting the ball in the back of the net.
The former Chorley forward was causing Brig plenty of problems, and he headed narrowly wide of the post from a free kick on 27 minutes.
Jamie Milligan’s side then grew into the game as the half came to a close.
Dan Martin had an effort deflected on 33 minutes, before Aaron Skinner curled a shot wide of the post.
Macauley Wilson then found the back of the net from a corner, but the flag was up for offside.
Brig also started the second half brightly. After Harris had fired over from inside the area for the visitors, both Skinner and Jacob Holland-Wilkinson came close for the hosts.
Then, on 60 minutes, Paul Dawson met Rhys Turner’s cross but his header went just over the bar.
On 71 minutes, the referee awarded the visitors a penalty.
Harris stepped up and placed the ball into the bottom left corner, beyond the full-stretch dive of Hewelt in the Brig goal.
Brig continued to push forward in an attempt to get back into the game late on.
Holland-Wilkinson was played through on goal on 86 minutes, but goalkeeper Liam Hughes got a glove to the ball before the on-loan Preston North End striker could get his shot away.
Dawson and Fin Sinclair-Smith both saw shots blocked in stoppage time, with Brig unable to find a goal that would have sparked hopes of a comeback in the closing stages.
Milligan’s side are next in league action on February 5, when they travel to Ashton United.