A three-goal blast in the first half ensured that Horden collected a hat-trick of UniBond League scalps when they beat Frickley on Saturday.
Horden have already beaten Telford and Warrington in the competition, and their first-half display showed their progress has been well deserved.
Manager Eddie Freeman said: "It was a superb performance. We said before the game that Frickley are a good footballing side and we had to get at them - and the players did exactly that.
"It was a fantastic day for the club, and the team seems to enjoy these big occasions. Anybody at home will do now."
Horden took the lead after just two minutes when Kevin Devine fired past the Frickley keeper from the edge of the box.
A few minutes later, James Huntley was brought down and Chris Pearson scored from the penalty spot.
Horden were in control from then on, and scored the third when Devine passed to Andy McKenna, who sidestepped a defender before shooting home.
Shildon, who reached the first round proper last season, earned a Wednesday night replay after they drew 3-3 at another UniBond League club, Radcliffe Borough.
Shildon were two goals up inside the first 20 minutes. Midfielder Adam Reid firing Shildon into the lead after the Radcliffe defence failed to clear, then Danny Richmond scoring the second from 25 yards.
But Radcliffe pulled one back when Simon Carden finished off a good move, then Richard Battersby ran though and chipped Shildon keeper John Jackson after 31 minutes.
Just after half time, Radcliffe went 3-2 up when Steve Foster scored from a Phil Denney cross, but Shildon didn't give up and Reid levelled with a low shot.
Manager Ray Gowan said: "We have still got every chance of going through, but we're still not firing on all cylinders. We battled back well."
Billingham Town looked as if they might be going through as they led Conference club Vauxhall Motors for more than an hour, but the visitors won 3-1.
Town got off to the best possible start when Lee Ure scored from a pass by David Turner, but then they proceeded to miss a string of chances, with Carl Chillingsworth, Ure, Jason Ainsley and Stuart Brightwell all missing.
And Town paid the penalty with six minutes left when James Olsen scored, and then Karl O'Donnell and Wayne McDermott rubbed salt in their wounds.
Manager Alan Robinson said: "We should have taken more of our chances. At half time we should have been at least 3-0 up, but their equaliser knocked our ends in."
Esh Winning went out bravely, by 3-2 at Lancaster City after being two goals down early on.
Peter Thompson headed home after just nine minutes, then Ryan Zico-Black fired the second.
But Esh fought back, and Andy Cuthbertson scored from a Ben Gawthorpe cross. However, Lancaster went 3-1 up through a Steve Jones shot, only for David Mawson to quickly reply for Esh, who were denied a draw by two fine saves by the home keeper.
Esh manager Barrie Fleming said: "The players gave everything. We can take a lot of pride from pushing a Conference side."
Dunston must also go to a replay after they drew 2-2 with Cammell Laird at Federation Park.
They took an early lead when Graeme Armstrong scored from a David Southern cross, but Cammell Laird equalised when Ian Morgan scored with a deflected shot after 39 minutes.
But within a minute Dunston were back in the lead when Steve Holmes headed in. However, the Scousers hit back in the second half with a shot by Chris Cooke.
Gateshead are definitely through after they beat Chorley 4-1 at the International Stadium.
Recent signing George Weatherly gave them an early lead from a Daniel Fox pass, then Paul Taylor scored from the spot after he had been brought down.
Jamie Vermiglio pulled a goal back for Chorley, who were finally killed off when Taylor raced clear to score the third. Neil Wilkinson scored in the dying minutes for the fourth.
Ashington lost 3-1 at home to Droylsden, Brian Smith equalising for Ashington in the first half.
Whitby's run ended when they lost 2-0 at home to Mossley, a division below them in the UniBond League. Chris Downey put Mossley ahead after 27 minutes, and after Whitby's Neil Bishop was red-carded for violent conduct, Downey fired a second.
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