Clitheroe fell to two home defeats over the week, shipping six goals.
On Saturday, the Blues conspired to lose a game they should have won, going down 3-1 against Colwyn Bay at Shawbridge.
But they were second best on Tuesday night against Clitheroe legend Neil Reynolds’ Bamber Bridge, who went fourth in the table with a 3-0 victory.
Charlie Russell headed over from a corner after thre minutes against Brig, who responded with Ally Waddecar spurning an opening created by Regan Linney.
Dan Mooney sent a shot just wide, before Linney forced a save from Chris Thompson from close range.
Brad Carsley had an effort blocked by Thompson, and three minutes before half-time, Mooney crossed from the right and Carsley fired Brig ahead.
Clitheroe started the second half brightly, but Thompson had to push a Mooney shot behind.
Linney hit the post, but just after the hour, Linney created another chance for Carsley and he made no mistake.
Just a couple of minutes later it was three when Mooney cut in from the right and scored from the edge of the box.
Colwyn Bay raced into a two-goal lead within eight minutes on Saturday, as Jamie Rainford netted from the spot, before Astley Mulhollandtook advantage of a slack backpass from Jacob Davis.
Kurt Willoughby hit the woodwork, but Clitheroe came out a changed team in the second half, and threatened to blow away the visitors.
They pulled one back on 53 minutes as Ryan Ellison’s cross was tucked home by Alex Newby.
But Bay sealed victory 17 minutes from time, with a full length diving header from Mulholland.
Clitheroe travel to face Evo-Stik First Division North leaders and promotion favourites South Shields on Saturday.
The Mariners – joint-managed by former Blackburn Rovers striker Graham Fenton – have won seven of their eight league games to date, and boast former Sunderland and Middlesbrough man Julio Arca.
The Blues then host Ramsbottom United at Shawbridge on Tuesday night.