The Yellows were made to rue what might have been as the replay took almost a role reversal from Saturday’s 2-2 draw at Cantilever Park as the hosts had the better of the game.
A strange goal direct from a corner inside the first 15 minutes gave Halifax a cushion and they made the game safe through Dayle Southwell in the second half to set up a trip to League Two side Morecambe.
The big pitch at the Shay contributed to a much different game than in the first tie on Saturday, as full-time Halifax flexed their muscles.
It was men against boys at times as the Yellows struggled to get a foothold in the match and retain the ball for a sustained period against the National League side, clearly rattled at being second best for large parts of the weekend’s encounter.
But for the first five minutes at least, there were signs of encouragement for the Yellows as Jake Kirby, their main threat throughout the match, made progress down the left and forced a corner within a minute of kick-off.
Nothing came of it and the closest they would go to scoring early doors was when a whipped cross by Alex Whittle was glanced well wide by Tony Gray.
Halifax gradually grew in to the game, striker Jonathan Edwards was starting to cause problems, and it was a foul on him that earned Mark Roberts the first yellow card of the match on 12 minutes.
They scored with their first chance, if you can describe it as that, as from a corner conceded by Whittle, Jordan Preston curled an inswinging delivery straight in to the back of the net inside Tony McMillan’s near post in somewhat bizarre circumstances.
Both sides had a couple of minutes to digest that opening goal as McMillan then spent time receiving treatment and looked set to come off to be replaced by 18-year-old Joe Williams, only to eventually hobble back to his goal and continue.
When the game restarted, Halifax almost doubled their lead instantly, Dayle Southwell feeding Edwards to shoot just wide with McMillan beaten.
Halifax were dictating the game but Kirby was providing a glimmer of hope for the Yellows at the other end, he took Dylan Vassallo’s ball down the left touchline and made his way towards the six yard box, forcing a corner.
Southwell had a couple of chances for Halifax before Matt Kosylo should have done better when released on the counter attack by Edwards, lofting the ball wide as he tried to beat McMillan.
The Yellows registered a shot on target through a simple Gray effort but were thankful to brave Dave Raven for ensuring they entered half time just a goal down.
The centre-back blocked on the line three times in one move in first half stoppage time, before adding a fourth for good measure moments later to deny Edwards, Southwell and Kosylo as the Yellows desperately clung on.
Warrington consolidated at the start of the second half, but had the same struggles in finding a foothold further up the pitch.
Their hopes were all but ended on 65 minutes when the tricky Kosylo fed the ball past a defender and it was swept home across the goalkeeper by Southwell for 2-0.
The Yellows had their best spell in the final quarter and had a couple of half chances, one when substitute Bohan Dixon had a drive towards goal blocked in the six-yard box, but ultimately Halifax were too strong and held out for the win comfortably.
Warrington return to action on Saturday in the FA Trophy against Prescot Cables at Cantilever Park.
Halifax Town: Johnson, Sellars, Clarke, Staunton, Kosylo, King, Southwell, Edwards, Preston, Skarz, Hanson. Subs: Rowley, Odelusi, McLeod, Lenighan.
Warrington Town: McMillan, Duggan, Whittle (Hughes), Garrity, Roberts, Raven, Mackreth (Amis), Evans, Gray, Kirby, Vassallo (Dixon). Subs: Beeley, Carden, George, Williams.
Pictures John Hopkins