Lethal finishing and relentless creativity from County brought a nine-goal annihilation as Stirling's initially spirited show disintegrated into sheer embarrassment.
Derek Adams' side, pumped with belief amid a run of five wins and a draw, was unchanged from last weekend's shock triumph at Dens Park.
The Binos' mission was to create a shock and land the kind of money-spinning quarter-final draw that might ease their well-publicised financial plight. County, though, were in ruthless mood and went straight for the jugular.
From Scott Morrison's free-kick, Alex Keddie tore in to the six-yard box to thump a header past the off-balance Stirling keeper. County surged two ahead with Michael Gardyne starting the move and finishing it after Garry Wood spotted his well-timed run into the box.
The ex-Celtic youth's finishing was again faultless as he lifted a 12-yard shot into the corner of the net. Gardyne's tenth of the season then became 11 after 20 minutes. The midfielder had only one thought as he tore onto a loose ball 22 yards out and ripped his shot high into the net.
Allan Moore's men were spirited and took the game to County in spells, but were stung again after 55 minutes.
Richard Brittain's swept ball across the face of goal from the right and Wood tore in front of the keeper to apply a simple close-range finish. Four minutes later, Albion were facing a rout as Wood struck the fifth low from the edge of the box. The sixth was tucked away from the spot by Brittain after Wood was downed in the box by Ross Forsyth.
Substitute Stuart Kettlewell forced in the seventh eight minutes from time after a Steven Watt header crashed off the under-side. And it was eight two minutes later as Scott Morrison's swirling free-kick from 35 yards eluded everyone from deep right. Wood wrapped up his hat-trick in the final minute.