Tabish Hussain was on target with a fine strike just before the break, but The Seahorses held on to progress.
Alex Zachariou deputised in holding midfield to replace the unavailable Dexter Ball, meaning Duke Witter regained his place in the starting eleven after Alex had donned the number 11 jersey at Emley.
Garforth started the better of the two sides with Witter coming close with a swerving strike which went inches wide after a corner kick was played back into the box from Whitley Bay keeper Dan Lister's half clearance. Matt Antcliff then got sight of goal when set up by Keiran Clayton on the edge of the box, but his low shot was straight at Lister. A Tabish Hussain free-kick in a good position then just cleared the bar.
It was against the run of play then, that the hosts scored two quick-fire goals around the 20 minute-mark that suddenly left The Miners with a mountain to climb. A corner from the left twice wasn't cleared, allowing Scott Lowery to put The Seahorses ahead despite Toby Wells' efforts to stop the ball crossing the line. Only a minute later it was 2-0 after Wells denied Lewis Suddick and the ball went straight to Matty Weirs who fired low into the net.
Town enjoyed another good spell towards the end of the half and were at least rewarded with a goal back. A Sam Barker shot from Witter's delivery was blocked in the six-yard box by Wayne Phillips, then on 40 mins it was 2-1 courtesy of a fine debut goal by Hussain. After a corner kick was cleared straight to him, Hussain teed himself up on the edge of the area and volleyed home beyond the dive of Lister.
Paul Marshall's side enjoyed plenty of the ball in the second half against the hosts who seemed happy to sit deep and counter. Antcliff's curling effort was deflected wide moments in, then Zachariou went close with a couple of 30-yard efforts which went narrowly wide.
The two sides traded chances with the next goal likely to be crucial. Ben Richardson's dangerous delivery into the six-yard box had to be headed clear by Jamie Barkway, then Hussain nearly grabbed his second when Lister palmed his 20-yard shot wide of the near post. Wells then made a good save to turn wide a Richardson strike. There were appeals for a penalty on 71 mins when Andrew Cartwright went down in the area, but the referee promptly waved play on.
Despite some decent approach play Town sadly lacked the quality in front of goal to bring the tie level. After a tricky foray into the box, Hussain's shot was straight at Lister, but he brought a good stop from him at the near post after Barkway's long throw was only half-cleared. The hosts did enjoy some good chances of their own, with Wells denying Suddick just inside the box after he got the better of Harry Viggars from a long ball forward. Viggars was then pushed forward for the remaining minutes but suffered the same frustrations as his attacking teammates when getting on the end of a couple of deliveries to the near post; he too being kept out by Lister.
The hosts should've made it three in the dying stages when substitute Cameron Brewis was supplied deep in the box with acres of space, but somehow skewed wide. In the end it mattered not, as The Seahorses successfully saw out the tie and leave Town once again to wonder what might have been.
With Tuesday's opponents Penistone being taken to a replay by City of Liverpool in their FA Cup tie, Tuesday's league match at the Bannister Prentice Stadium is now postponed, but a friendly match at home to Selby Town will take it's place (kick-off 7.30pm).