Playing away to City of Bath, who were unbeaten this season going into this third-round tie, the holders went behind early in the first half to a drag flick at a short corner.
However, the Sarnians were level by half-time thanks to a Zak Damarell goal.
The second half was a cagey affair and the match looked to be heading towards a dreaded penalty shoot-out, but with 10 minutes to go Ben Cormack scored with an emphatic drag flick to seal a 2-1 win for Guernsey.
They have been drawn away to Stourport in the quarter-finals, which are due to be played on 1 March.
