Kilmarnock will face Queen's Park in the Scottish Cup fourth-round.
Angelo Alessio's men have entered into the competition that they are aiming to win for the first time since 1997.
Ray Montgomerie captained the side to victory that day at Ibrox, with Paul Wright scoring the vital goal in a 1-0 win over Falkirk.
Italian boss Alessio is aiming to get Killie to Hampden for the first time since 2012, when they defeated Celtic 1-0 in the League Cup final thanks to a Dieter Van Tornhout header.
Killie were close to booking a spot at Hampden earlier this season as they hosted Hibernian in a Betfred Cup quarter-final clash.
But a penalty shootout proved to be Killie's downfall as they lost out and the capital men booked their Hampden spot.
Ties to be played on the weekend of Saturday, January 18
Full draw:
St Mirren v Broxburn
Kilmarnock v Queen's Park
Hearts v Airdrie
Alloa v Inverness
Livingston v Raith
Auchinleck/Arbroath v Falkirk
Dundee United v Hibs
Ayr v Ross County
Aberdeen v Dumbarton
Bonnyrigg v Clyde
St Johnstone v Morton/Brora
Hamilton v Edinburgh City
Partick v Celtic
East Kilbride v BSC Glasgow
Dundee v Motherwell
Rangers v Stranraer
