The Ayrshire side will join Auchinleck Talbot and Clydebank in the last 32 where they will face Championship high-flyers Arbroath at Gayfield.
The match against Highland League side Brechin was replayed after a 1-1 draw at Glebe Park, and it was the visitors from Angus who took the lead on 37 minutes when Kieran Inglis side-footed home a volley.
Darvel were level on the stroke of half-time when Darryl Meggat headed home from a corner and the home side took the lead with 11 minutes remaining when Ryan Thomson turned a shot into the net.
Brechin refused to accept their fate and levelled through a wonder strike from Murray Mackintosh with two minutes remaining.
Darvel, however, prevailed on penalties, winning 5-4 to progress to the next round and continue their first ever Scottish Cup run.