In their first game of 2015, the Hillmen overcame some rustiness, a strong wind and a sodden pitch to come back from an early blow to continue their pursuit of leaders Runcorn Linnets.
GNE started disjointedly as they tried to deal with the conditions, and had a warning on seven minutes when Hudson cut in from the left but shot over the bar from the edge of the area.
It was not heeded though, as the home side took the lead in the tenth minute.
The ball was worked to the left and Hudson put in a terrific cross to the penalty spot that Liam Crellin-Myers stooped to head past Greg Hall.
Glossop tried to respond quickly and Jason Carey’s snapshot forced a good save from Craig Ellison in the Congleton goal.
North End gradually began to get a grip of the game but their final delivery was lacking quality.
However, on 31 minutes they were back on level terms when a mis-hit shot fell kindly to Kieran Lugsden who swept the ball home from 12 yards out.
North End proceeded to dominate proceedings in the second half with Ellison twice saving well from Eddie Moran, while Richardson drove just wide after making space for himself.
Finally the goal came on 64 minutes when Tom Bailey got behind the defence and scored at the second time of asking after his initial effort was blocked.
Bailey then prodded wide of the post before rectifying that miss late on with the crucial third goal.
A foul in the box on Sam Hind gave Bailey the chance to net from the penalty spot and he duly tucked it away.
Saturday sees GNE travel to Worksop Town in the FA Vase fourth round. Winners of the last-32 tie will receive £2,000 in prize money.