The Bedfordshire side put in a dominant display on Friday night, racing into a 5-1 lead by half-time.
Peacock also had his hat-trick by the interval, netting three goals within the first 40 minutes of The FA Cup tie.
Friday's FA Cup Preliminary Round results
Romulus 3-1 Causeway Utd
Mickleover Sports 3-1 Thurnby Nirvana
Thetford Town 0-3 Norwich Utd
Staines Lammas 1-8 Barton Rovers
Beaconsfield 5-1 Didcot Town
Wantage Town 3-2 Kidlington
By Simon Collings
Three more goals followed in the second-half, with Peacock adding two more and Dale Turney rounding off the victory with a 35-yard thunderbolt.
Beaconsfield SYCOB were also comprehensive winners in their FA Cup clash, but they were made to work harder than the scoreline suggests.
The Buckinghamshire club overcame Didcot Town 5-1, but after an even first-half Beaconsfield only found themselves 2-1 up.
However three second-half goals, including a brilliant long-range effort from Ollie Jones, ensured that Beaconsfield progressed to the next round.
Elsewhere, there was plenty of drama during Wantage Town and Kidlington’s FA cup encounter.
At half-time Wantage Town were 2-0 up, but an all-action second 45 minutes saw two red cards and three more goals.
Kidlington levelled the tie thanks to efforts from Jake Quainton and Ryan Curtin, but with 15 minutes remaining it was Tom Melledew who made himself the hero by scoring a late winner for Wantage.
There were also 3-1 wins for Mickleover Sports and Romulus who defeated Thurnby Nirvana and Causeway United respectively.
While Norwich United also booked their place in the next round of the FA Cup after running out 3-0 winners away to Thetford Town.
