Dundee survived a huge scare against Lowland League side Bonnyrigg Rose to reach the Scottish Cup third round.
The hosts equalised in the 94th minute, then fell behind in extra time before recovering to progress 3-2.
Fellow Championship side Alloa Athletic are out after losing 3-2 at home to Cove Rangers of League One.
Forfar Athletic and Stranraer struggled past non-league sides, while East Fife routed Tranent Juniors 5-1 and Fraserburgh defeated Banks O'Dee 2-1.
Twelve ties were postponed because of the frozen conditions. The draw for the third round - which will include Premiership teams - is on Sunday at 11:00 GMT.
Dundee trailed to a Bonnyrigg team three tiers below them when Lee Currie converted a 25th-minute penalty at Dens Park.
James McPake's men dominated the second half, and twice hit the woodwork, but were 90 seconds from an embarrassing exit until Jonathan Afolabi bundled home.
Another Currie penalty restored Bonnyrigg's lead before Lee Ashcroft and Osman Sow netted to finally overcome the underdogs.
Elsewhere, Cove twice came from behind to shock Alloa, who led through an Alan Trouten penalty and Cameron O'Donnell strike.
Jamie Masson and Rory McAllister replied for the visitors, who snatched a dramatic victory when Ryan Strachan's free-kick found the top corner.
Stranraer did it the hard way against Lowland League leaders Kelty Hearts, who were in control at half-time at Raith Rovers' Stark's Park after Nathan Austin's lob and a Kallum Higginbotham penalty.
Thomas Orr soon reduced the deficit and Scott Robertson headed Stranraer level before Ruari Paton's stoppage-time penalty completed the comeback.
Forfar fell behind to East of Scotland League outfit Linlithgow Rose after 11 minutes thanks to Kyle Wilson's opener.
Murray MacKintosh quickly levelled, but the visitors held out until extra time when Martyn Fotheringham and a Jordan Allan double sent Forfar through.
East Fife veteran Scott Agnew scored an 18-minute hat-trick - and had a role in all five goals - after Steven Thomson's free-kick gave Tranent an early lead.
The 33-year-old netted a penalty then crossed for Craig Watson to head the hosts in front by half-time. Two further Agnew goals followed before he rounded off a sparkling performance by teeing up Kevin Smith to score.
Highland League Fraserburgh recovered from Michael Philipson's opener for junior team Banks O'Dee to prevail with a Scott Barbour header and Jamie Beattie strike.
And on Sunday, League 2 Edinburgh City pulled off a minor shock by beating Airdrieonians, from a division above. Ouzy See scored the only goal in North Lanarkshire.