Lowland League side Spartans were drawn a home tie in the next round of The William Hill Scottish Cup against Berwick Rangers or Albion Rovers.
Cup holders St Johnstone face an away tie to Queen of the South in the fifth round of the competition.
The draw, which was made at the Scottish Football Hall of Fame at Hampden Park, paired the Saints with the 2008 runners-up Queen of the South, while Lowland League outfit Spartans were rewarded for their victory over Morton with a home tie against either Berwick Rangers or Albion Rovers.
Celtic face Dundee at Dens Park in one of two all-Premiership ties, as Partick Thistle host either St Mirren or Inverness Caledonian Thistle. There’s an all-Championship clash too, with Rangers facing Raith Rovers in a repeat of the 2014 Challenge Cup Final.
2010 winners Dundee United face a trip away to either Stranraer or Dunfermline Athletic while Hibernian host Arbroath, who recorded a 5-0 victory away to Bo’ness United in the previous round.
Falkirk, who defeated Cowdenbeath at the Falkirk Stadium on Saturday, will be at home once more in the next round, against Annan Athletic or Brechin City.
William Hill Scottish Cup fifth-round draw:
Queen of the South vs St Johnstone
Rangers vs Raith Rovers
Dundee vs Celtic
Hibernian vs Arbroath
Falkirk vs Annan Athletic/Brechin City
Stranraer/Dunfermline Athletic vs Dundee United
Partick Thistle vs St Mirren or Inverness Caledonian Thistle
Spartans vs Berwick Rangers/Albion Rovers
