James Boyd gave Brig a 14th-minute lead, which was cancelled out by Mason Duffy’s equaliser in the 37th minute.
But the visitors were back in front a minute before the break through Brad Carsley.
And Carsley wrapped up the victory with his second and Brig’s third seven minutes from time.
Elsewhere in the division, Clitheroe won 5-2 at Atherton Collieries, with George West (2), Alex Newby (2) and Kurt Willoughby (penalty) on target for the visitors.
Kendal went down 2-1 at home to Brighouse Town, Ben Thomas with their late consolation goal.
In the NPL Premier, Lancaster won 5-0 at Whitby Town, Samuel Bailey (2), Charlie Bailey, Mamadou Djabi and Paul Jarvis the scorers.
Jack Muldoon’s first-half goal secured a third straight National League victory for AFC Fylde at Bromley.
But Kevin Davies’ Southport suffered a 1-0 National League North defeat at the hands of hosts FC United on Sunday.
Tom Greaves hit the post for United in the seventh minute as the home side started strongly.
Joel Senior then fed Greaves, who fired in what turned out to be the game’s only goal in the 12th minute.
Southport rallied and Jason Gilchrist was denied by a fine save by home keeper Lloyd Allinson before the break.
Gilchrist’s brother Adam came on as a late sub for United, who held on to claim the points.
In the NWCL Premier, Charnock Richard won 2-1 at Abbey Hey, but Burscough lost 1-0 at home to Widnes.