A double from John McAtee made it a comfortable evening for the Oakwell outfit in their FA Cup replay in Sussex.
The League One side got off to the best possible start after just three minutes. A cross from Adam Phillips was only parried by keeper Lewis Carey, and Nicky Cadden followed up from close range.
Barnsley looked assured and doubled their lead seven minutes later. Aiden Marsh crossed in from the byline, and McAtee was left unmarked in the area to power his shot past Carey.
Although Horsham attempted to get a foothold in the tie, the contest was all-but over after 27 minutes.
A long ball from Jordan Williams found McAtee on the edge of the box, and with great touch he lobbed the onrushing Carey for his second of the evening – and the third for Barnsley.
A weak effort from the onrushing Lucas Rodrigues was the first notable chance for the home side.
Phillips forced Carey to tip over the bar as Barnsley successfully navigated a potentially tricky contest.