A goal in each half from Jordan Preston and Dayle Southwell booked Halifax’s trip to the League Two side in the first round, and pocketed £25,000 to boot.
As it turned out, Warrington’s best chance was on Saturday. An upset was never on the cards here.
Town boss Jamie Fullarton said his side would have to improve if they wanted to remain in the competition, and they did.
It was ironic that Town took the lead through Jordan Preston’s corner going straight in at the near post, considering the chances they squandered after that.
The contest was a role reversal of Saturday’s game, with Town in control and Warrington struggling to make an impression.
Town were much sharper and quicker in open play, while Warrington lacked the attacking thrust and fluidity that had caused Halifax so many problems three days previously.
If the question at half-time on Saturday was how were Warrington not in-front, here it was how were Town only 1-0 up.
Jonathan Edwards went close to doubling the hosts’ lead shortly after Preston’s opener when he was slipped through by Southwell, but scooped his shot wide.
Matty Kosylo saw a shot brilliantly blocked after a lovely ball by Jacob Hanson had sent Preston away down the right.
More terrific play by Hanson saw him out-skill his man before picking out Southwell near the penalty spot, but he fired wide.
Southwell then had a low shot saved after good footwork earned him some space inside the box.
Another flowing move saw Edwards find Southwell, who then played in Kosylo cutting in from the left, but he chipped the ball over the bar.
The chances kept coming, and going.
The best Warrington could muster in the first-half came just before the interval when Tony Gray worked a yard of space but Sam Johnson comfortably saved his shot across goal.
The first-half was encapsulated at its conclusion, when the impressive Preston and Hanson combined well to send the ball in from the right, and Southwell, Edwards and Kosylo all saw shots blocked by Warrington defender David Raven; chances spurned and determined defending.
Town remained in control after the interval, although not quite replicating their attacking intensity of the opening 45.
A few more passes went astray and the pace dropped off a little, but Warrington didn’t muster much a response.
So when Southwell swept the ball in left-footed from Kosylo’s pass 15 yards out, not only had Town finally got the cushion their play had merited, but Warrington looked down and out.
Former Town man Bohan Dixon - remember him? - had a goalbound shot blocked with 15 minutes to go, but the result was never in doubt.
Halifax: Johnson, Hanson, Clarke, Skarz, Sellers, King, Staunton, Preston (Odelusi 81), Southwell, Kosylo, Edwards. Subs: Rowley, Lenighan, McLeod.
Scorers: Preston (15), Southwell (66)
Shots on target: 6
Shots off target: 6
Warrington: McMillan, Duggan, Roberts, Raven, Whittle (Hughes 51), Mackreth (Amis 81), Evans, Garrity, Vassallo (Dixon 65), Gray, Kirby. Subs not used: Beeley, Carden, George, Williams.
Shots on target: 3
Shots off target: 1
Referee: Andrew Miller
Town man of the match: Jordan Preston