Darius Osei and Joao Gomes both netted twice for the Mariners, with Dylan Mottley-Henry adding his name to the scoresheet in the second half.
Defeat means the Brig have now lost five of their last six league matches, conceding 21 goals in the process.
In the night’s other action, Lancaster City upset Hyde United with a 2-1 win at Ewen Fields.
First half goals from Dale Whitham and Nic Evangelinos proved enough for the Dolly Blues as they picked up a third victory in their last four matches.
Jack Redshaw did pull one back for the Tigers eight minutes after half-time, but they soon had Callum Spooner sent off for a second bookable offence and were unable to find an equaliser, meaning they drop to third in the table.
Despite the win, Lancaster's night was overshadowed by a nasty injury for the visitors' Calen Gallagher-Anderson, who suffered a dislocated ankle.
Results - Tuesday 22 November
Hyde United 1-2 Lancaster City
South Shields 5-0 Bamber Bridge
Photo credit: Kev Wilson Photography/South Shields
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