Brora had not played since their 2-1 first-round win against Camelon on January 11, hours before Scottish football was suspended below the top two men’s divisions.
The Highland League remains suspended, with Brora having played just three league matches, but they stunned Robbie Neilson’s Championship leaders – Scottish Cup runners-up in the past two years – at Dudgeon Park.
Brora took the lead in the 12th minute when Jordan Macrae found the top corner following a break down the left.
Incredibly, Brora regained the lead six minutes later when Martin Maclean headed home from a corner.
The home team held on without major late scare to set up a third-round tie at home to Stranraer on April 3.
Falkirk set up a trip to Celtic Park after coming from behind to win 2-1 at Arbroath. Thomas O’Brien gave the hosts an early lead but Charlie Telfer levelled with a neat finish just before the break.
Arbroath dominated the second half but the Bairns broke in the 87th minute and Kai Fotheringham struck.
Inverness secured a Highland derby against Ross County but they had a late scare in a narrow 3-2 win at Buckie Thistle.
First-half goals from James Keatings and Sean Welsh had Caley Thistle 2-1 ahead until Callum Murray levelled with six minutes left. Daniel Mackay put the Championship side back in front two minutes later to set up the trip to Dingwall.
Partick Thistle secured a trip to Tannadice to face Dundee United following a 3-0 home win against Cowdenbeath. Shea Gordon, Zak Rudden and Connor Murray were on target.
Raith Rovers will travel to Livingston after winning 2-0 at Stirling thanks to goals from Gozie Ugwu and Dylan Tait.
Dumbarton will host Aberdeen after a 4-0 win over Huntly thanks to a brace from Jamie Wilson and one apiece from Ryan McGeever and Ross Forbes.
Ayr also won 4-0, at Elgin, following first-half goals from Joe Chalmers, Michael Moffat and Luke McCowan (two). They will now host Clyde, for whom David Goodwillie was on target in a 2-0 win over Keith.
Stenhousemuir will host Kilmarnock after Mark McGuigan’s goal earned a 1-0 victory at Peterhead.
Craig Johnston hit a hat-trick as Montrose won 7-1 at Nairn to set up a trip up the north-east coast to face Fraserburgh.
Motherwell will take on former Fir Park midfielder Paul Lawson’s Formartine United in Pitmedden after the Highland League side beat Annan 3-1 on penalties after a 1-1 home draw.
Lewis Strapp scored the winning penalty as Morton set up a trip to face East Fife following a shoot-out after a drab goalless draw with Dunfermline.