Hearts booked their place in Tuesday's second round-draw for the Petrofac Training Cup after beating Annan 3-1 at Tynecastle on Saturday.
Billy King, Osman Sow and Callum Paterson scored in the first half but Scott Davidson claimed a late consolation.
Falkirk enjoyed a 7-1 victory against local rivals East Stirlingshire at Ochilview, with Rory Loy and Blair Alston both notching doubles. Will Vaulks, Alex Cooper and Botti Biabi were also on target, with David McKenna replying.
Greig Spence hit a hat-trick as Alloa defeated Arbroath 4-1 at Gayfield. Stephen Simmons scored early for the Wasps and the hosts' only consolation was a late own goal.
Livingston won a thriller 4-3 after extra time against Queen of the South at Palmerston, with substitute David Robertson scoring the decisive goal five minutes from the end. Andy Dowie, Iain Russell and Michael Paton netted for QOS, with Craig Sives, Danny Mullen and Myles Hippolyte also scoring for Livingston.
A Frank McKeown double and a stoppage-time goal from Sean Winter saw Stranraer storm back from two goals down at half-time to beat Dumbarton 3-2 at Stair Park. Jordan Kirkpatrick and Mark Gilhaney scored for the Sons.
Albion Rovers twice came from behind thanks to goals from summer signings Ally Love and John Gemmell to draw 2-2 in the Lanarkshire derby with Airdrieonians before winning 4-2 on penalties at the Excelsior Stadium. Liam Watt and Nathan Blockley scored for the Diamonds.
Alan Trouten and Ryan Ferguson struck in extra time as Brechin City beat Cowdenbeath 3-1 at Central Park. Sean Higgins opened the scoring but Robert Thomson levelled for City.
Peterhead won 3-0 at Montrose, who finished the game with nine men. Andy Rodgers, Rory McAllister and Jamie Stevenson scored in the first half while Graham Webster and Garry Wood saw red for the home team.
Barry Ferguson made a winning start as Clyde boss as goals from Scott McManus and John Sweeney saw Ayr United beaten 2-0 at Broadwood.
Stirling Albion beat Elgin City 3-0 at Borough Briggs, with Gordon Smith grabbing a double after Darren Smith had opened the scoring. Elgin had Matthew Cooper sent off.
Jon McShane and Ewan Moyes got the goals as East Fife edged out Forfar 2-1 at Bayview. Dale Hilson pulled one back for Dick Campbell's team.
Morton defeated Lowland League winners Spartans 1-0 at Cappielow thanks to a first-half goal from Cameron O'Neil.
Stenhousemuir went down 3-1 after extra time away to Highland League champions Brora Rangers, with Zander Sutherland netting a hat-trick. Martin Grehan got the Warriors’ goal from the penalty spot.
The match between Dunfermline and holders Raith Rovers at East End Park fell victim to a waterlogged pitch after a torrential downpour.
Berwick Rangers beat Queen's Park on penalties on Friday night while the Rangers v Hibernian tie goes ahead on Tuesday August 5, live on BBC ALBA at 7.35pm.
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