Max Watters headed the Tykes in front in the first half, but the Hornets equalised courtesy of Shamir Fenelon’s spectacular finish.
James Hammond’s spot-kick then stunned Oakwell, but Fabio Jalo’s fabulous curling effort saw the hosts level on the stroke of half-time.
Mael De Gevigney headed Barnsley in front again in the second half. The Tykes then wasted a hatful of chances to put the tie to bed before second half Horsham substitute Tom Richards tapped into an empty net following a lightning Hornets counter attack.
The two sides will meet again at the Camping World Community Stadium on Tuesday, November 14.
Here is a selection of excellent photos from Oakwell courtesy of Natalie Mayhew, ButterflyFootie.
1. Barnsley FC v Horsham FC in the FA Cup: 38 more brilliant match and fan photos as never-say-die Hornets hold League One Tykes in roller coaster first round tie
The best of the action from the pitch and the stands from Horsham's 3-3 draw at Barnsley in the FA Cup first round Photo: Natalie Mayhew, ButterflyFootie
2. Barnsley FC v Horsham FC in the FA Cup: 38 more brilliant match and fan photos as never-say-die Hornets hold League One Tykes in roller coaster first round tie
The best of the action from the pitch and the stands from Horsham's 3-3 draw at Barnsley in the FA Cup first round Photo: Natalie Mayhew, ButterflyFootie
3. Barnsley FC v Horsham FC in the FA Cup: 38 more brilliant match and fan photos as never-say-die Hornets hold League One Tykes in roller coaster first round tie
The best of the action from the pitch and the stands from Horsham's 3-3 draw at Barnsley in the FA Cup first round Photo: Natalie Mayhew, ButterflyFootie
4. Barnsley FC v Horsham FC in the FA Cup: 38 more brilliant match and fan photos as never-say-die Hornets hold League One Tykes in roller coaster first round tie
The best of the action from the pitch and the stands from Horsham's 3-3 draw at Barnsley in the FA Cup first round Photo: Natalie Mayhew, ButterflyFootie