Holders Celtic have been given a home draw against Stirling Albion in the fourth round of the Scottish Cup.
Juniors Linlithgow Rose travel to Queen of the South, while Highland League outfits Huntly and Cove Rangers face Dundee and Ross County, respectively.
SPL rivals Falkirk and Aberdeen meet, while Hearts entertain Motherwell and Hibernian host Inverness.
Third Division East Stirlingshire will make a money-spinning trip to Ibrox to take on Rangers.
Last year's losing finalists Dunfermline, who were also relegated from the SPL, launch their bid to return to Hampden with an away tie at Partick Thistle.
St Mirren will face Third Division strugglers Dumbarton at Love Street.
"We will be underdogs and that will be an unusual feeling for us as we are favourites in almost every junior game we play"
First Division sides Morton and Clyde will each fancy their chances of causing an upset after being drawn at home to SPL sides Gretna and Dundee United.
And the reward for coming through a third-round replay for Airdrie United and Queen's Park is a home tie with Kilmarnock.
First Division leaders Hamilton were drawn at home to Brechin or East Fife, St Johnstone will tackle Raith Rovers, and Livingston face Cowdenbeath.
Linlithgow became the first junior side to reach the fourth round after seeing off Newton Stewart, Spartans and Dalbeattie Star.
And manager Jim Sinnet admits that he would have preferred a big-money tie with Celtic or Rangers than a trip to Dumfries to meet a First Division side.
"It will be a difficult game," he said. "We will be underdogs and that will be an unusual feeling for us as we are favourites in almost every junior game we play. The pressure is on them.
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"But hopefully we can force a replay and take them back to Linlithgow with a bit of luck.
"If we could get into the last 16, it would be a massive achievement.
"We will take over 1,000 fans and they will spur us on.
"It's been vitally important that the junior sides who entered won a few games, otherwise we would have had egg on our face."
Queens manager Gordon Chisholm did not seem to be too perturbed about the prospect of facing a junior side.
"I'm quite pleased with a home time," he told BBC Sport.
"It will be difficult but it's one we will be expected to win."
Meanwhile, Stirling Albion manager Allan Moore hoped to avoid a mauling at Celtic Park.
"It's the draw everyone in the lower divisions was looking for because it brings the money in," he said.
"But we went there a few years ago and managed a respectable 7-0 defeat. We know it will be difficult.
"Going to Parkhead will be a big occasion for our boys, but we won't go there and sit back."
Scottish Cup fourth-round draw
Hamilton v Brechin City or East Fife
St Mirren v Dumbarton
Partick Thistle v Dunfermline
Falkirk v Aberdeen
Hibernian v Inverness CT
Huntly v Dundee
Hearts v Motherwell
Rangers v East Stirlingshire
Queen of the South v Linlithgow Rose
Morton v Gretna
Airdrie Utd or Queen's Park v Kilmarnock
St Johnstone v Raith Rovers
Cove Rangers v Ross County
Clyde v Dundee United
Livingston v Cowdenbeath
Celtic v Stirling Albion
Matches to be played on weekend of 12/13 January.
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