Having powered into 2-0 lead inside the opening six minutes, the Rebels somehow let their hosts back into proceedings at 2-2 and, in the end, owed their semi-final berth to strikers Ansil Bushay and Mark West.
First, Bushay tapped is a 74th minute effort after West had sneaked through before unselfishly squaring for the former City player to score and then West added the decisive fourth himself.
Having deftly controlled a long free-kick the prolific marksman span away from his marker before arrowing a low shot just inside do post for his second of the night.
Bat even after re-establishing their two-goal cushion, Slough sloppily conceded a third that left the score line doing little to reflect their overall dominance.
They had begun it awesome fashion, as West dipped in his first following a Catlin kick-in, and then with their title rival still reeling, Catlin rifled a 20-yard drive into the top comer for the second with just six minutes or the dock.
Then, after Stone had been denied by both goalkeeper and post, and Bushay, Sayer and West with two headers had squandered excellent opportunities, two mix ups at the heart of the visitors' defence handed St Albans a lifeline through Gurney and Brett they could well have extended but for Clark's 39th minute penalty miss.
St Albans City Line up
Gareth Howells, Dean Murphy, Kevin Mudd (Martin Duffield), Steve Clark, Barry Blackman, Shaun Brett, Detszi Krusznski (Allan Cockram), Steve Scott, Andy Polston, Martin Gurney, Andy Driscoll.