Kilmarnock will start their Scottish Cup journey away to either Peterhead or Stenhousemuir in the third round.
The Blue Toon square off against the Warriors, from League Two, in a rearranged clash, with the winner set to host Alex Dyer's side.
The last time the Ayrshire side met League One Peterhead was in the 2007/08 season when Colin Nish, Frazer Wright and Steven Naismith gave Killie a 3-0 win in the League Cup.
More recent was the last clash against Stenhousemuir when Killie hosted them in their first game as defending League Cup winners.
But it was a disaster for Kenny Shiels' men as they fell to a 2-1 defeat, with now-Hurlford United striker John Gemmell scoring the winner.
Ayrshire rivals Ayr United still have a second-round tie to navigate away to Elgin City and should they see that through, they will play Highland League Keith or League One Clyde.
Full draw:
Forfar v Edinburgh City
Dundee United v Partick/Cowdenbeath
Livingston v Stirling or Raith
Camelon/Brora Rangers/Hearts v Stranraer
Peterhead/Stenhousemuir v Kilmarnock
Rangers v Cove Rangers
Celtic v Arbroath/Falkirk
Ross County v Buckie Thistle/Inverness CT
Queen of the South v Hibernian
Dumbarton/Huntly v Aberdeen
East Fife v Morton/Dunfermline
Dundee v St. Johnstone
Hamilton v St. Mirren
Elgin/Ayr United v Keith/Clyde
Fortmartine United/Annan v Motherwell
Fraserburgh v Nairn County/Montrose
