Kilmarnock were made to work their passage by stuffy second division opponents at Glebe Park.
Brechin had goalkeeper Craig Nelson to thank for keeping the SPL side at bay in the first half but he ran out of heroics after the break.
Brechin were denied in eight minutes when striker Gary Twigg expertly lofted the ball over Alan Combe. He turned to celebrate only to see the assistant referee call him back with a raised flag.
Kilmarnock were determined to take the sting out of the game and in 13 minutes Medhi Taouil picked out Frazer Wright inside the box but his powerful header was saved by Nelson.
Brechin almost snatched the lead 60 seconds later.
Full-back Willie Dyer romped forward and fed Twigg who clipped the ball through for Ian Diack, but his low drive through the six-yard box was too quick for everyone.
Nelson kept his side in the game in 16 minutes, this time diving to his near post to pluck the ball away after Allan Russell had planted a header goalwards.
The 37-year-old goalkeeper was in inspired form and made another crucial intervention on the half-hour when Bryson looked set to score with a drive from inside the area.
Willie Gibson replaced Russell on the resumption.
Kilmarnock finally found the goal they so desperately needed after 58 minutes.
Taouil's free kick from the right caught Brechin square and they left Wright in far too much space, allowing him to slot a low shot beyond Nelson.
Kilmarnock's clinched the tie seven minutes later with a sublime strike.
Garry Hay linked well with Gibson on the left and the former's low cross landed perfectly for Craig Bryson, who flicked an unstoppable shot into the top corner.
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