Newly-crowned Eastern Counties Two champions Billericay rattled up 47 second-half points without reply - after leading only 8-5 at the interval - as winger Mike Coxford grabbed three tries and replacement Andy White two.
Billericay began brightly, gaining good possession at scrums and line-outs - and their opening score came from one such throw-in.
Richard Holdgate won it and the ball was fed along the backs for Coxford to go over.
Kevin Harmon's penalty after 20 minutes increased the lead, before a lapse let in a Cooperians side battling to finish second for an unconverted try.
Billericay, though, ran amok when playing down Brent-woodians' slight slope in the second half.
Skipper Paul Daly got the first of their seven further tries - with Harmon kicking six more conversions - when he scored off the back of a rolling maul.
Then White crossed the line twice within 10 minutes, Coxford added two to complete his treble, and Glenn Smith notched a brace of his own.
The handsome win provided ideal practice for one of the biggest games in Billericay's history this Saturday - the home Tetley's Vase last-four tie against Scarborough for a place in the Twickenham final. Billericay have been eagerly preparing their pitch.
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