Jed booked their Forsyth Cup semi-final spot last Saturday.
A Barrie Melrose header put them ahead inside 15 minutes and shortly after Chandler doubled the lead, tucking away a Swailes cut back.
Chirnside pulled one back on the half-hour mark.
But Jed went up a gear in the second half. Swailes smashed home a third from the edge of the box and Jeffrey made it 4-1 with a 25-yard strike.
The visitors scored twice inside the final 15 minutes to make it a nervy final few minutes for Jed.