The Tykes made sure there would be no giant-killing in front of the ITV cameras with a dominant first half display at the Camping World Community Stadium.
Nicky Cadden and John McAtee (2) put Barnsley 3-0 up inside 30 minutes, although the Hornets were much-improved in the second half.
Daniel Ajakaiye went close three times in the second period, but Horsham were unable to find a thoroughly-deserved consolation goal.
Here is a selection of excellent photos from the Cup clash courtesy of Natalie Mayhew, ButterflyFootie.
Daniel Ajakaiye went close three times in the second period, but Horsham were unable to find a thoroughly-deserved consolation goal.