In front of a 327 crowd at the Butcher`s Arms, the Tigers came back from being a 10th minute Jacques Kpohomouth goal down to win, thanks to Karl Jones seven minutes after the break and a Max Leonard brace on 71 and 87 minutes.
Scarborough Athletic missed the opportunity to go second when they suffered a 3-2 defeat at their Flamingo Land Stadium to fourth-placed Bamber Bridge, who are now four points behind them.
An excellent crowd of 1,123 saw Michael Coulson give Boro a 15th minute lead. But Brig turned round 2-1 in front, thanks to Lewis Nightingale after 28 minutes and Adam Roscoe four minutes later.
Regan Linney then made it 3-1 on 66 minutes, although Jack Johnson's second for the home side in stoppage time meant a few anxious minutes for the Lancastrians.
Tadcaster Albion hold the final play-off spot and Trafford are just a point behind in seventh, but neither were able to win on Saturday.
Taddy were held to a 0-0 draw at home by mid-table Atherton Collieries, while Trafford shared a 2-2 draw – also at home – against third-bottom Skelmersdale United.
Aaron Burns gave the home side the lead on the half-hour mark but Jordan Darr sent Skem into the break on level terms with a 41st minute equaliser. Ali Brown restored Trafford's lead four minutes after the restart, only for Phil Mooney to level once more on the hour-mark.
Clitheroe are two points behind Trafford now in eighth after edging out fourth-bottom Brighouse Town by the odd goal in five at Shawbridge.
The visitors took an early sixth minute lead through Jack Normanton. Joe Mitchell levelled 10 minutes later and then Jack Egan after 29 minutes and Kurt Willoughby seven minutes before the break, took the Blues 3-1 ahead. Mo Ibrahim 'won' the second half for the Yorkshire side but it came in stoppage time.
Goole AFC remain a point adrift at the bottom after losing 3-1 at Glossop North End.
The Hillmen's Callum Chippendale's 28th minute strike separated the teams at the interval. Declan Howe levelled six minutes into the second half but a second for Chippendale from the spot on 71 minutes and then Jack Higgs 12 minutes from time, took the game away from the Vikings.
Image courtesy of Matthew Appleby/Twitter
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