Kevin Phillips' side had led 3-0 with 20 minutes remaining, and although Byron Harrison scored twice from the penalty spot for the Dabbers, the Mariners held on for the win.
Their advantage at the top of the division stands at eight points with nine left on the table, after Bamber Bridge fell to a 5-2 defeat at FC United of Manchester.
A Max Cane double helped the Reds come from behind to lead 3-1 at half-time, with further goals from Michael Donoghue and Luke Griffiths sealing the win after visiting forward Fin Sinclair-Smith kept up his fine scoring form for the Brig shortly before the hour mark.
Warrington Town took advantage of the result at Broadhurst Park to leapfrog Bamber Bridge and climb to second with a 3-0 victory over Ashton United.
The Robins had won four in a row heading into the fixture but proved to be no match for the Yellows, as goals from Josh Amis (2) and Luke Duffy saw them extend their unbeaten run to 21 matches.
Elsewhere in the race for the top five, Gainsborough Trinity came from behind to beat Lancaster City 2-1, while Radcliffe were forced to settle for a point away at Liversedge.
Hyde United also remain three points adrift of the play-offs after they fell to a surprise 2-1 defeat at home to struggling Morpeth Town on Good Friday.
Goals from Sam Fishburn and Matty Cornish helped the Highwaymen move three points clear of the relegation zone.
Meanwhile, Joe Hardy's goal three minutes after half-time helped Marine to a 1-0 win at Marske United, and a third minute goal from Alex Duhameau saw Matlock Town beat Atherton Collieries by the same margin.
Mo Touray struck twice as Warrington Rylands came from behind to beat already-relegated Belper Town, while Guiseley came from a goal down to draw 1-1 with Stalybridge Celtic, who remain in the relegation zone.
And in the only other game of the round, Kaiman Anderson scored his 11th goal of the season as Stafford Rangers defeated Whitby Town 1-0 at Marston Road.
There will be another full round of fixtures on Easter Monday, with the majority of teams in the division having just three regular season fixtures left to play.
Results - Friday 7 April
Hyde United 1-2 Morpeth Town
Warrington Rylands 3-1 Belper Town
Results - Saturday 8 April
FC United of Manchester 5-2 Bamber Bridge
Guiseley 1-1 Stalybridge Celtic
Lancaster City 1-2 Gainsborough Trinity
Liversedge 1-1 Radcliffe
Marske United 0-1 Marine
Matlock Town 1-0 Atherton Collieries
South Shields 3-2 Nantwich Town
Stafford Rangers 1-0 Whitby Town
Warrington Town 3-0 Ashton United
Photo credit: Mark Lee
Keep up-to-date with our exclusive email newsletters.
Subscribe