The Hillmen maintained their excellent form on Tuesday night with a solid 2-0 win away at fifth-placed Squires Gate.
Jason Carey notched both goals on a night when Lee Blackshaw was making his 200th outing for North End.
After a first-half in which Chris Willcock’s men failed to break down a stubborn Squires’ defence, they came out fighting in the second as they aimed to keep up the pressure on league leaders Runcorn Linnets.
And indeed they did, with Carey netting after a through-ball from Tom Bailey.
GNE, who are into the last 16 of the FA Vase and face a meeting with Chesterfield in the quarter-finals of the Derbyshire Senior Cup next week, then upped the ante in search of a crucial second goal.
That duly arrived midway through the second half and it was once again Carey who found the net, this time heading home from a corner.
North End maintained a clean sheet to ensure their exceptional defensive record remains intact.
They have conceded just ten league goals all season and although they remain 12 points behind Linnets, they do have five games in hand.
Glossop host 1874 Northwich in the league on Saturday.
Then next Tuesday (February 3) the DSC last-eight clash with Chesterfield takes place at Surrey Street.
The League One club played a fairly strong side in the last round when they beat Graham Street Prims 5-2.
The winner will face Matlock at home in the semi-finals of the competition.
North End: Hall, Richardson, Russell, Lugsden, Young, Parker, Blackshaw, Carey (Halfacre), Bailey (Hind), Lugsden, Moran (Gresty).
Subs not used: Grimshaw, Turner.