Barnsley quickly put this tie to bed with a professional first half showing, ensuring a second round trip to Sutton United.
In a dominant first 45, Neill Collins' side eased to a comfortable victory in this Emirates FA Cup first round replay.
Looking far too good for the opposition once again, this time, the Reds put their chances away and booked their place in round two.
Just three minutes had been played before we took the lead. It came via good work down the right flank involving Jordan Williams and Adam Phillips, with the latter swinging over a cross that the Horsham 'keeper flapped at, allowing Nicky Cadden to volley in unopposed.
It was 2-0 inside 10 minutes as another deep cross, this time from Aiden Marsh from the opposite wing saw John McAtee volley in, again, unmarked at the back stick.
He added a third Reds goal when after Williams found him on the edge of the box, he chipped the goalkeeper with a sublime finish.
HALF TIME: Horsham 0-3 Barnsley
There was an early chance for the hosts in the second half when Rodrigues was played into the box, but under pressure, his shot was weak and easily collected by Ben Killip.
Adam Phillips saw the goalkeeper tip over a goalbound strike after some wonderful football out wide from substitute Vimal Yoganathan.
Another sub, Sam Cosgrove sent a header just wide at the back stick, as Herbie Kane's inswinging corner picked him out, but chances for either side were few and far between in the second period.
It had been a comfortable, professional display from the Reds, and they'll now face Sutton United (of Sky Bet League Two) away from home on Saturday 2 December.
FULL TIME: Horsham 0-3 Barnsley
Killip, Williams (O'Keeffe), de Gevigney, Shepherd, McCart, Cadden (Dodgson), Kane, Connell (Yoganathan), Phillips, Marsh (Watters), McAtee (Cosgrove).
Unused: Flavell, McCarthy, Cotter, Ackroyd.
