Dundee will host Celtic in one of two all-Premiership ties after the draw for the fifth round of the Scottish Cup.
Partick Thistle have to wait until St Mirren face Inverness Caledonian Thistle in Tuesday's replay before knowing their visitors to Firhill.
Holders St Johnstone are away to Championship side Queen of the South.
Rangers host Championship rivals Raith Rovers, while Lowland League side Spartans entertain Berwick Rangers or Albion Rovers from League Two.
Dundee manager Paul Hartley, whose side have drawn 1-1 with Celtic at home and lost 2-1 away this season in the league, reckons his charges can cause another upset.
"It couldn't have came any tougher than Celtic but we're at home," he told BBC Scotland. "It's a game everyone will look forward to.
"The two games we've played against them there's not been a lot between the two sides and we'll have some confidence and try to win the game.
"If you're going to win the Cup you have to beat the best sides and we'll have to be at our best to knock Celtic out."
Spartans have already defeated two Scottish Professional Football League sides - League Two outfit Clyde and then League One leaders Greenock Morton - in this season's competition.
|Spartans chairman Craig Graham on his side's Scottish Cup draw|
|"To be honest we were looking for one of the bigger teams but it's a home tie, so it's exciting, and it's against the teams that are closest to us, albeit a league above us."|
And manager Douglas Samuel is targeting another scalp from the Scottish Professional Football League.
"Being honest, I'd have liked to play a Premiership side away from home, but if we were going to get a home draw we wanted someone we were going to be competitive against," he told BBC Scotland.
"Make no mistake, Berwick and Albion Rovers will be delighted with the draw and will be the favourites, but it's a game we can go into with some optimism and hope.
"Who knows, we might just be the first non-league team in modern times to reach the last eight."
Spartans chairman Craig Graham echoed those sentiments.
"It maybe wasn't the draw we wanted," he said.
"To be honest we were looking for one of the bigger teams but it's a home tie, so it's exciting, and it's against the teams that are closest to us, albeit a league above us."
By the time St Mirren and Inverness settle their replay, half of the 12 Premiership clubs will have exited the competition before the fifth round.
At least two more will have also gone out ahead of the quarter-finals, leaving a maximum of four in the last eight.
The other surviving top-flight side, Dundee United, have been drawn away from home against the winners of an all-League One replay between Dunfermline Athletic and Stranraer.
Hibernian host League Two leaders Arbroath, while Championship rivals Falkirk await the winners of the replay between bottom-tier Annan Athletic and League Two side Brechin City.
Scottish Cup fifth-round draw
Queen of the South v St Johnstone
Rangers v Raith Rovers
Dundee v Celtic
Hibernian v Arbroath
Falkirk v Annan Athletic or Brechin City
Stranraer or Dunfermline Athletic v Dundee United
Partick Thistle v St Mirren or Inverness Caledonian Thistle
Spartans v Berwick Rangers or Albion Rovers
Ties to be played on the weekend of 7/8 February.