The Easter Road side defeat Turriff United away 3-0 on Sunday to book their place in the last 16.
St Mirren defeated Albion Rovers but needed extra time to win their third-round tie.
The fourth round sees teams from Wales and Northern Ireland enter the competition for the first time.
It’s a radical revamp for the tournament formerly known as the Challenge Cup.
Welsh Premier League champions The New Saints are away to Forfar, while runners-up Bala Town have been drawn at home to Alloa.
Northern Irish Premiership champions Crusaders are at home to Livingston. Linfield, the runners-up in Northern Ireland, are away to Queen of the South.
Ties are due to be played on the weekend of 8/9 October.
The draw was made at Oriam, the new Scottish centre of sport in Edinburgh.
Irn Bru Cup fourth round draw:
Bala Town v Alloa Athletic
Forfar Athletic v The New Saints
Crusaders v Livingston
Queen of the South v Linfield
Hibernian v St Mirren
Dunfermline Athletic v Queen’s Park
Ayr United v Falkirk
Stranraer v Dundee United