Newcastle made one change for the cup Replay with Callum Lovatt Saturday's hero starting at the back replacing the missing Luke Dennis.
Castle initially looked more comfortable against Congleton’s physical attacking style than in the previous game, dealing with several early chances for the hosts early on.
However, they still struggled to get any advantage out of their own long ball game, with the host’s centre-backs comfortable under the high ball.
Newcastle was aggrieved early on that no further action was taken when Congleton striker Thomas Hampton appeared to elbow Callum Lovatt after being flagged offside.
Soon after, Congleton had the first real chance of the match, as a fine cross saw the header drift inches wide of the post.
The hosts went close again minutes later, as Newcastle keeper Joe Slinn did just enough to ensure another header went over the bar.
However, Newcastle was ahead soon afterwards as Nathan Morley drove into the box, and fed Jake Lovatt, who fired into the far corner to put Castle one to the good.
Newcastle had a chance to double their lead moments later, but the header was straight at Congleton keeper David Parton.
The visitors did manage to contain Congleton for the rest of the half, but Hampton did force a save from Slinn with the last play.
Despite an early Congleton burst, Newcastle had the better of the early second-half exchanges, with Jake Lovatt forcing a save from Parton.
Slinn then had to be alert to gather another Congleton header from a drop ball, after another excellent cross by the hosts. Congleton were starting to build pressure, but it was Newcastle who doubled their lead, as Ethan Vale latched onto a loose ball to hammer home a long-range strike into the net to extend the Castle lead.
In response, Congleton brought on Aaron Johns, and he was on the scoresheet minutes later, as he poked home off a Newcastle defensive mix up.
With that lifeline, Congleton ramped up the pressure with a series of corners and throws, before Duffy tapped in at the back post for the equaliser.
Newcastle was beginning to look troubled, and was being pinned in their own half, with their only let-off coming when Duffy hit the bar.
Congleton then went to the other end of the field for Johns to head home with the goal to take them to the next round.
Newcastle had one last opportunity from Vale’s free kick, but it come to nothing and with that the tie was over.