Guernsey FC went out of the FA Trophy as two second-half goals sent South Park through to the next round.
Kieran Lavery broke the deadlock midway through the second-half, tapping in for the hosts after capitalising on Simon Geall's loose header back to goalkeeper Chris Tardif.
With time ticking away, Asa Rixon-Nicholls doubled the South Park advantage, turning in from a corner.
The Green Lions remain without a win away from the island in 2016.
Meanwhile, Wednesday's match between Guernsey and Chipstead at Footes Lane has been postponed because of the latter's FA Trophy replay.