Barnsley opened the scoring through Max Watters but the Hornets hit back through Shamir Fenelon and James Hammond’s penalty.
But the Tykes restored parity before the break thanks to a Fabio Jalo wonder-strike.
Mael De Gevigney headed Barnsley in front just after the hour mark, but second half substitute Richards sensationally levelled with nine minutes to play to force an unlikely replay.
Here’s a selection of pictures from the game at Oakwell courtesy of Getty Images.
1. Barnsley FC v Horsham FC in the FA Cup: Valiant Hornets claim well deserved draw in FA Cup classic - fan and match gallery
Horsham fans celebrating after the Emirates FA Cup First Round match between Barnsley and Horsham at Oakwell Stadium. Photo: Ben Roberts Photo
2. Barnsley FC v Horsham FC in the FA Cup: Valiant Hornets claim well deserved draw in FA Cup classic - fan and match gallery
Kadell Daniel of Horsham pre-match warm up ahead of the Emirates FA Cup First Round match between Barnsley and Horsham at Oakwell Stadium. Photo: Ben Roberts Photo
3. Barnsley FC v Horsham FC in the FA Cup: Valiant Hornets claim well deserved draw in FA Cup classic - fan and match gallery
Daniel Ajakaiye of Horsham pre-match warm up ahead of the Emirates FA Cup First Round match between Barnsley and Horsham at Oakwell Stadium. Photo: Ben Roberts Photo
4. Barnsley FC v Horsham FC in the FA Cup: Valiant Hornets claim well deserved draw in FA Cup classic - fan and match gallery in
Barnsley FC vs Horsham FC in the FA Cup: Heroic Hornets claim well deserved draw in FA Cup classic - the match in pictures (Photo by Ben Roberts Photo/Getty Images) Photo: Ben Roberts Photo