Having earned a replay with a 2-2 draw on Saturday, the Yellows progressed in some style thanks to a Jamie McDonald brace and a late Tony Gray strike.
It sets up a mouthwatering local derby against Altrincham at Cantilever Park on Saturday December 16 in the first round proper.
There was just one change to the Yellows line-up from Saturday, with Steve Jennings returning for James Barrigan.
The first half followed a similar pattern to the second half at the weekend, with Warrington looking most comfortable.
A mazy run by Dylan Vassallo down the right saw him cut inside and beat four men before getting a ball across that was cleared off McDonald’s toes.
It didn’t take long for the deadlock to be broken though, McDonald taking the ball on from a Vassallo pass and then lifting it over the onrushing keeper for 1-0 on 11 minutes.
Time passed without much to note until Yellows skipper James McCarten hobbled off on the half hour mark to be replaced by Jack Higgins, who was used as a makeshift striker off the bench on Saturday.
Despite the change, the Yellows then hit their strongest period of the game. Both Brad Barnes and Sean Williams had shots at goal with a couple of Vassallo corners also causing problems.
The second goal came on 33 minutes and it was McDonald again, showing great strength to hold off his man and then as he was losing balance to his left, he managed to open his body and steer it past the keeper in to the far corner.
McDonald’s confidence was through the roof and his weaving run ended in a shot that was well blocked. Such was Warrington’s dominance that Tamworth were forced in to a change before the break, bringing on Callum Powell to enable them to switch to a 4-4-2.
Although Steph Morley curled a free-kick just over the bar in first half injury time, the visitors will have been pleased to get in the dressing room.
Tamworth were perhaps fortunate not to be reduced to 10 men early in the second half when Luke Jones hauled back Vassallo when through on goal, the referee perhaps judging that the 30 yard distance from goal meant a yellow was justified.
The Yellows somehow didn’t make it three on 50 minutes when Shaun Rowley saved first from McDonald, then from Barnes and then adjusted brilliantly to save a deflected Williams shot with his leg.
But the National League North side eventually flexed their muscles and as the hour mark passed, they were well on top.
They thought they had a route back in to the game when Darryl Knight diverted the ball goalwards and somehow Tony McMillan stopped it from crossing the line.
McMillan was also at his best on 69 minutes when a Higgins slip let Connor Taylor in, saving with his legs, before Liam Goulding cleared off the line.
Tamworth huffed and puffed but just couldn’t find the break through, and as time wore on, a comeback looked less likely.
The Yellows wrapped things up in the 89th minute, Gray finishing well with his left foot after a break involving Scott Bakkor and Barrigan.
Warrington return to league action on Saturday with a tricky trip to fourth place Shaw Lane.
Warrington Town: McMillan, Carden, McKeown, Jennings, McCarten (Higgins), Goulding, Williams, Barnes, McDonald (Barrigan), Gray, Vassallo (Bakkor). Unused subs: Davis, Paynter.
Tamworth: Rowley, Burns, Morley, Deeney, Jones, Lane, Upton (Powell), Verma, Kotwica (Reid), Taylor, Knight. Unused subs: Shaw, Walters, Coulson.