A full list of the most recent match against non-league opposition for each of the 42 current SPFL clubs. Edinburgh City have not faced non-league opposition since joining the SPFL in 2016. Note that Hibs and Partick Thistle will both face non-league sides in the 4th Round of this season's Scottish Cup.
25/01/1971 - Aberdeen 5-0 Elgin City (Scottish Cup)
09/02/1985 - Inverness Thistle 3-0 Kilmarnock (Scottish Cup) [v Brora 10/02/18]
26/02/1992 - St Johnstone 3-0 Inverness Caledonian (Scottish Cup)
06/12/1997 - Inverness Caledonian Thistle 3-1 Whitehill Welfare (Scottish Cup)
07/01/2012 - Heart of Midlothian 1-0 Auchinleck Talbot (Scottish Cup)
24/10/2015 - Stirling Uni 0-2 Queen's Park (Scottish Cup)
28/11/2015 - Falkirk 4-1 Fraserburgh (Scottish Cup) [v Formartine/Cove 10/02/18]
07/02/2016 - East Kilbride FC 0-2 Celtic (Scottish Cup)
19/07/2016 - Alloa Athletic 4-0 Cove Rangers (League Cup)
22/07/2016 - East Stirlingshire 0-3 Rangers (League Cup) [v Fraserburgh 30/01/18]
26/07/2016 - Motherwell 3-0 East Stirlingshire (League Cup)
30/07/2016 - Ross County 7-0 Cove Rangers (League Cup)
22/10/2016 - Arbroath 4-1 Stirling Uni (Scottish Cup)
22/10/2016 - Berwick Rangers 2-3 Hawick Royal Albert (Scottish Cup)
03/12/2016 - Beith Juniors 0-6 Greenock Morton (Scottish Cup)
03/12/2016 - Formartine United 4-0 Annan Athletic (Scottish Cup)
06/12/2016 - Dumbarton 0-1 Bonnyrigg Rose (Scottish Cup)
21/01/2017 - Bonnyrigg Rose 1-8 Hibernian (Scottish Cup)
21/01/2017 - Partick Thistle 4-0 Formartine United (Scottish Cup)
15/07/2017 - East Kilbride FC 1-3 Hamilton Accies (League Cup)
18/07/2017 - Queen of the South 0-0 East Kilbride FC [1-4 pens] (League Cup)
19/07/2017 - Buckie Thistle 0-3 Dundee United (League Cup)
22/07/2017 - Dundee 2-0 Buckie Thistle (League Cup)
15/08/2017 - Raith Rovers 3-0 Brora Rangers (Challengee Cup)
15/08/2017 - Stenhousemuir 0-2 Cove Rangers (Challenge Cup)
02/09/2017 - Buckie Thistle 0-3 Dunfermline Athletic (Challenge Cup)
14/10/2017 - Cowdenbeath 0-1 East Kilbride FC (Scottish Cup)
14/10/2017 - Elgin City 3-1 Edusport Academy (Scottish Cup)
14/10/2017 - Keith 0-3 Clyde (Scottish Cup)
14/10/2017 - Montrose 4-1 Stirling Uni (Scottish Cup)
14/10/2017 - Peterhead 9-0 Colville Park (Scottish Cup)
14/10/2017 - Stirling Albion 3-5 Lothian Thistle HV (Scottish Cup)
18/11/2017 - Airdrieonians 2-3 Cove Rangers (Scottish Cup)
18/11/2017 - Banks O'Dee 2-6 Ayr United (Scottish Cup)
18/11/2017 - Buckie Thistle 2-3 Brechin City (Scottish Cup)
18/11/2017 - East Kilbride 3-4 Albion Rovers (Scottish Cup)
18/11/2017 - Formartine United 1-0 Forfar Athletic (Scottish Cup)
18/11/2017 - Livingston 2-0 Glenafton (Scottish Cup)
18/11/2017 - Lothian Thistle HV 1-7 St Mirren (Scottish Cup)
18/11/2017 - Stranraer 0-1 Brora Rangers (Scottish Cup)
20/01/2018 - East Fife 0-1 Brora Rangers (Scottish Cup)
craigkillie's post in Last game against a non-league side was marked as the answer