In the home game for Jersey, played at East Grinstead, the match went to penalty flicks after Bournville scored in the final minutes of the game to level the scores 2-2.
Following some well timed saves from Jersey keeper Paul Duckworth Jersey emerged 6-5 winners on penalties.
They will now play either Kingston-upon-Hull or Old Wulfrunians in the final on Sunday 26 April.
