The Bucks did not get going in this third qualifying round tie at Cantilever Park until the final few minutes. It was too little too late.
Bohan Dixon and Ben Garrity struck for the Northern Premier leaders. Daniel Udoh scored in second half added-on time for the Bucks but, ultimately, the Yellows were well worth the win and the £15,000 prize money.
Warrington enjoyed the lion's share of possession early on. Telford, whenever they got the ball, went direct - looking to find top scorer Udoh or his strike partner Amari Morgan-Smith with high balls downfield.
The Yellows, who had former Shrewsbury man David Raven at centre-half, dealt with that approach easily for the most part though. And that was not surprising as they have kept eight successive clean sheets in the league.
The Bucks' best chance of the first half fell to Salop loanee John McAtee. Morgan-Smith found space on the right flank and cut the ball back to the teenager. He should have hit the target but could only fire wide on the stretch.
Steph Morley started at left-back for Telford after several weeks on the sidelines with a calf problem - and the cross for Dixon's opener came from his side. Jack Mackreth delivered the ball to Dixon, who gobbled up the opportunity. A very disappointing goal to concede, especially given the fact they let one in at the same time to lose at Blyth Spartans last weekend.
The Bucks - probably following some harsh words from boss Gavin Cowan - began the second period with a bit more energy, but still could not cause the Yellows any significant problems.
And the hosts doubled their advantage shortly after the hour mark. The visitors were caught cold from a clever corner, Garrity taking advantage with a powerful drive.
Telford looked to find a way back by making a few substitutions - Adam Dawson, Darryl Knights and Andre Brown coming on. Warrington cleared a Brown effort off the line before Udoh got his 11th of the campaign - although goalkeeper Tony McMillan appeared to be fouled.
The Bucks then pumped several balls into the box in search of a leveller, but the crosses lacked quality. And that was the story of the game for Cowan's charges.
24 - Good chance for Telford to take the lead. Amari Morgan-Smith cuts the ball back to McAtee, who takes a touch before poking wide on the stretch from 10 yards.
45 - Goal! Warrington 1-0 Telford. Bohan Dixon scores for the hosts. Jack Mackreth floats a cross towards the penalty spot. Target man Dixon rises above Theo Streete and heads past Max Bramley. Fine finish. Fairly poor defending.
64 - Goal! Warrington 2-0 Telford. Ben Garrity fires past Bramley. It's a corner routine straight from the training ground - played low to the edge of the box and then poked to Garrity, who finishes well on the turn. The Bucks are staring down the barrel.
86 - Bucks substitute Andre Brown has an effort cleared off the line by Mitch Duggan.
90 - GOAL! Warrington 2-1 Telford. The Bucks pull one back through Daniel Udoh. He taps in after a melee in the box.
Warrington (4-4-2): McMillan, Duggan, Roberts (c), Raven, Whittle (Hughes, 65); Mackreth, Garrity, Evans, Kirby; Dixon (George, 84), Gray (Amis, 81)
Subs not used: Beeley, Benjamin, Carden, Speare
Telford (4-4-2) Bramley; White, Streete, Sutton (c), Morley; McQuilkin (Dawson, 67), Royle, Deeney, McAtee (Knights, 67); Udoh, Morgan-Smith (Brown, 82)
Subs not used: Smith, Cowans, Barnes-Homer, Wycherley (gk)
Referee: Richard Aspinall (Lancashire)