It was an 18-minute spell at the end of the first half which did the trick, Corey Browne netting a hat-trick and Gary Abbott striking twice more - once from the penalty spot after the Essex side had taken the lead in the 21st minute through Scott Mallon.
Sub Lloyd Owusu added the sixth for the Rebels in the 81st minute, missing an open goal opportunity and hitting the base of the upright among half a dozen other chances for Slough.
Persistent rain made footholds uncertain and handling - as Tilbury's tiny keeper Mark Boxall demonstrated-was like juggling with ice cubes.
Slough made an altogether too dainty start and their over-complex passing movements on such an unpredictable surface were soon found wanting.
The route to success seemed writ large as Garry Smart's low shot in the ninth minute saw Boxall unable to hold at the first attempt.
But a more direct approach was not forthcoming until after the Isthmian Leaguers, who held their own for the opening 25 minutes, had shaken the Rebels by taking the lead.
Mallon, who had earlier glanced a header from a free kick just wide of the mark, was on hand at the far post to fire in Lee Goodwin's first time cross after Slough had only half cleared a long thrown in.
Tilbury almost added a second moments later when Danny Whybrow chased in for a hanging cross but hooked a tricky volley past the target.
The first time Slough whipped in a cross, courtesy of the tireless Gary Brazil, Browne swooped in to head past Boxall from close range to level the scores after 27 minutes.
Abbott put Slough ahead from the penalty spot when he was impeded by Boxall after being put through in the 36th minute.
And Abbott set up the second for Browne two minutes later, cutting in from the left and squeezing an angled drive past Boxall at the near post.
Boxall's problems continued despite confusion from a free kick in the 44th minute, Bolt miscuing after Brazil's dummy, but Browne completing his hat-trick with a glance off his head which saw the ball dribble through the hapless keeper's gloves and over the line.
Slough's fifth goal a minute later also went the long way round. Another Bolt free kick this time nodded back by Cliff Hercules only for Terry Angus to strike the upright with his header with the incoming Abbott stabbing home from two yards.
Though it was one-way traffic in the second half, Slough saw Matt Stowell, who hit the crossbar, Brazil and Abbott all fail to turn chances into goals.
The introduction of first Mark West, then Owusu, added further interest to the tie which was fast losing momentum.
There was warm applause when West - making his 125th appearance for Slough - swapped places with Browne, but there-no mistaking for whom it was intended.
West's snappy running and nimble footwork were still there, but the conditions did the Slough striker no favours, nor did the flashing studs in some of the tackles he withstood.
Clearly it will take a little more time for West's confidence to return, but his second excursion in the first team this term will have whetted his appetite for a regular place and put others on their guard.
With only two goals against in the past nine matches, the quest for goals for has become the priority for the Rebels. This half dozen will do them nicely for starters.
Tilbury Line up
Boxall, Howard, Smith, Cornthwiate, Lester, Goodwin, Dann, Mallon, McCann, Whybrow, Harrison. Subs: Gower (30, for Harrison), Harris (66, for Dann), Rees (72, for Whybrow).