Jordan Connerton opened the scoring for Lancaster in the ninth minute but Brig levelled through a Jamie Milligan penalty.
Regan Linney gave Brig a 2-1 lead just before the break as he netted a 44th minute goal.
Jacob Gregory levelled for the hosts in the 77th minute and Mayers popped up with a late winner.
Elsewhere in the division, Clitheroe’s game at Ramsbottom, and Burscough’s trip to Prescot Cables fell victim to the weather.
Kendal Town were beaten 3-2 at Colne.