Dundee United, Inverness, Queen of the South, Dunfermline, St Mirren, Dumbarton and Cove Rangers won to reach the third round of the Challenge Cup.
Both Northern Irish sides in round two, Crusaders and Linfield, also won their ties but Republic of Ireland's Bray Wanderers lost to Elgin City.
Welsh team Connah's Quay Nomads lost 2-1 to Dumbarton after extra-time.
All of the Premiership under-20s sides were knocked out while Falkirk beat Sligo Rovers 2-1 on Saturday night.
Holders Dundee United went in front against Alloa Athletic through Patrick Nkoyi's penalty but Kevin Cawley equalised before stoppage-time goals by Paul McMullan and Willo Flood averted extra-time.
Inverness Caledonian Thistle beat Aberdeen U20 4-2 with Riccardo Calder, Liam Polworth, David Raven and Carl Tremarco on target for the Highlanders. Sebastian Ross and Bruce Anderson netted for the hosts and both teams had a man sent off - Frank Ross for the Dons and Charlie Trafford for Inverness.
David Healy's Linfield got the better of hosts Spartans with a Louis Rooney penalty and Stephen Lowry's effort outweighing Blair Atkinson's consolation for the Lowland League side.
Crusaders led Motherwell U20 through Philip Lowry but the visitors went 2-1 up with David Turnbull and George Newell scoring at Seaview. However, two late goals from Billy Joe Burns secured a 3-2 win for Crusaders.
Highland League Cove went three up against Hamilton Academical U20 with Jamie Masson opening and Mitch Megginson scoring twice, including a penalty, and Jack Breen replying for Accies.
Stephen Dobbie netted twice in Queen's 5-0 win away to Berwick Rangers, with Shaun Rooney, Derek Lyle and Chris Kane also scoring.
Gavin Reilly also scored a brace as St Mirren beat Hearts U20 in Paisley. John Sutton got the Buddies' third after Rory Currie had replied for Hearts.
Nicky Clark scored two of visitors Dunfermline Athletic's three goals against Buckie Thistle, Andy Ryan getting the other.
Lewis Vaughan was a double scorer in Raith Rovers' 4-0 defeat of Ross County U20, Bobby Barr and Liam Buchanan also on target.
Russell McLean's penalty and Rory McAllister's effort secured Peterhead a 2-0 win over Annan Athletic.
Christopher Dodd and Jordan Allan scored as Elgin overcame Bray Wanderers.
The first of the day's ties, Dumbarton v Connah's Quay Nomads, was the last to finish due to extra-time. Callum Morris put the visitors ahead from the penalty spot but David Wilson levelled nine minutes before the end of regulation time and new signing Dimitris Froxylias marked his debut with a goal to send the Sons through.
On Friday, Stranraer won 2-0 against Partick Thistle U20 with Ryan Wallace and Danny Stoney on target.
And, on Tuesday, Montrose beat Ayr United on penalties in the first of the second-round ties.
The final second-round tie takes place on Sunday with Welsh side The New Saints hosting Scottish Championship outfit Livingston.
Saturday unless stated
Ayr United 1-1 Montrose (aet, 5-6 pens) (Tue)
Stranraer 2-0 Partick Thistle U20 (Fri)
Aberdeen U20 2-4 Inverness Caledonian Thistle
Berwick Rangers 0-5 Queen of the South
Buckie Thistle 0-3 Dunfermline Athletic
Crusaders 3-2 Motherwell U20
Dumbarton 2-1 Connah's Quay Nomads (aet)
Dundee United 3-1 Alloa Athletic
Elgin City 2-0 Bray Wanderers
Hamilton Academical U20 1-3 Cove Rangers
Peterhead 2-0 Annan Athletic
Raith Rovers 4-0 Ross County U20
Spartans 1-2 Linfield
Sligo Rovers 1-2 Falkirk
St Mirren 3-1 Hearts U20