Goals from Lewis Alessandra, Dylan Mottley-Henry (2), Gary Liddle and Mackenzie Heaney mean the Mariners are now eight points ahead of second-placed Hyde United with three games in hand.
Meanwhile, Warrington Town climbed to third in the table after extending their unbeaten run to 11 matches.
The Yellows recorded a second 2-0 home victory in the space of four days as goals in either half from Tom Hannigan and Jordan Buckley saw them past Lancaster City.
Radcliffe remain in fifth after a 4-2 win at home to Belper Town, while Gainsborough Trinity kept pace in the fight for the play-offs after hitting Marske United for six.
Liam Waldock, Curtis Durose and Fraser Preston all scored twice for the Holy Blues, with Adam Boyes grabbing a double in reply for the Seasiders at the Northolme.
Elsewhere, a second half finish from Jorome Slew earned Matlock Town a 1-0 win at Nantwich Town, while Matt Van Wyk scored a dramatic 97th minute winner as 10-man FC United of Manchester stole all three points at home to Guiseley.
There were also 1-0 victories for Marine and Morpeth Town, while Atherton Collieries bagged their first league win in seven matches as Adam Rooney and Jay Fitzmartin helped them past Warrington Rylands.
Results - Tuesday 7 February
Atherton Collieries 2-0 Warrington Rylands
FC United of Manchester 1-0 Guiseley
Gainsborough Trinity 6-2 Marske United
Marine 1-0 Stalybridge Celtic
Nantwich Town 0-1 Matlock Town
Radcliffe 4-2 Belper Town
South Shields 5-2 Liversedge
Warrington Town 2-0 Lancaster City
Whitby Town 0-1 Morpeth Town
Photo credit: Kev Wilson
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