Former Brentford trainee Lewis Ferrell gave his old side the perfect start when he handled in the box for Alan McCormack to make no mistake from the spot.
The Bees extended their lead just after the half-hour mark when Jake Reeves rounded off a slick five-man move to slot home coolly under Swans keeper Kyle Merson.
The game was over before the break when Kadeem Harris picked up the ball on halfway and ran on to rifle a 30-yard rising drive into the top corner.
Marcello Trotta made it four-nil just after the interval when he guided McCormack's precision right-wing cross over the keeper as Brentford turned the screw on the Skrill South outfit.
Staines' only real chance in a one-sided contest came after 68 minutes when Jerel Ifil bundled Max Worsfold's teasing free-kick wide when well placed.
Substitutes Will Grigg and Farid El Alagui both went close for the hosts before Clayton Donaldson rubbed salt in the wounds with a cheeky backheel to make it five-nil in time added on.