A goal in each half cost Bamber Bridge dear as they lost their third game on the bounce in league and cup competitions.
Brig were eager to take advantage in their only remaining home league match this month when they took on the Tamesiders.
However, as things turned out, the four games in 10 days were starting to take their toll on the home side.
Danny Dignan who proved to be a thorn in the Brig side all evening had his free-kick saved well by Brig keeper Andy Banks.
For the second game running offside decisions cost Brig as Anthony Murt had the ball in the net from Alex Porter's free-kick but it was ruled out.
Murt and Porter had half-chances for Brig before Mossley took the lead on 38 minutes when Graham Kay headed home from six yards.
The visitors were lifted by the goal and should have scored from chances for Nick Booth, Dignan, and Danny Self.
Brig appeared to run out of ideas by playing route one football but it almost paid off when substitute Neil Zarac headed narrowly wide from a Tom Ince cross.
Mossley grabbed their second of the evening when leading scorer Mark Fish curled his shot accurately past Banks.
Brig tried valiantly to get something out of the game with Ince having his shot spilled by Mossley keeper Andy Robertson and then Murt was unable to take advantage as the ball went clear.
- Bamber Bridge: Banks, Nay (Zarac 67), Kennedy (Black 67), McCann, Tong, Steel, Brown (Mason 82), Flitcroft, Murt, Porter, Ince.
- Attendance 174
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