Horsham twice took the lead through deaf-mute striker Lee Farrell who firstly got sent clear by a great ball and secondly capitalising on a terrible mistake from goalkeeper Dorus de Vries.
Horsham may have had a penalty in the very first 15 seconds, Kevin Austin the culprit with a poor challenge inside the area. Protests though were waved away.
There were 3 goals in the space of 5 minutes putting with Farrell putting Horsham in the lead but within 70 seconds, Darren Pratley equalized only for Farrell again to put Horsham in the lead after Dorus de Vries' awful blunder.
In the 37th minute, Swansea levelled after much pressure on the Horsham goal, Britton finishing well after great build up.
Jason Scotland all but made sure of progression the the Third Round after being set up by Anderson and the T&T striker finshed into the corner of the net.
Half Time - Swansea City 4-2 Horsham FC
Swansea returned for the Second Half the way they left the First with Paul Seuke doing well in the Part-Timers goal.
City then added the fifth with Pratley playing a fine ball across the face of goal with Robinson tapping in.
Swansea then had a goal wrongly disallowed, Substitute Guillem Bauza turning and hitting the post and the Scouser followed up but for some unknown reason, the referee blew up to disallow.
Soon enough the 6th came through Warren Feeney from 25 yards which just had too much power for Paul Seuke.
Many good chances came, Bauza, and Orlandi coming close with Andy Robinson hitting the post but the home fans had to be satisfied with 6 of the Finest. Third Round, Here We Come!
Man Of The Match - Darren Pratley