Alan Trouten's debut double for Clyde consigned Annan to defeat in their first match as a Scottish Football League side.
Former Queen's Park player Trouten netted a penalty on the hour mark before his clever chip sealed a 2-0 Challenge Cup win over the SFL newcomers.
Irn-Bru First Division promotion favourites Dundee suffered a shock first-round defeat at Second Division Alloa.
Both sides missed several chances before Chris Townsley headed home a Jamie Stevenson cross in the 59th minute and the on-loan Morton forward turned from provider to scorer with seven minutes left.
Mickael Antoine-Curier pulled one back with two minutes left but the home side held out.
St Johnstone also suffered an early exit as they lost 2-1 to Second Division champions Ross County.
Second-half goals from David Winters and Sean Higgins meant Collin Samuel's late goal was in vain.
Roberto Landi enjoyed a successful start to his Livingston reign as the West Lothian side beat Stranraer 4-0 at Almondvale.
Leigh Griffiths netted a double and second-half strikes from Anthony McParland and Joe Hamill finished off Derek Ferguson's side, who had Kevin Nicol sent off.
Paul Di Giacomo struck the winner on his Airdrie debut as the Diamonds came from two goals down at half-time to beat Dumbarton 3-2.
Dunfermline recorded a comfortable 3-0 win over Stirling and two early goals inside a minute from Damon Gray and Mark Roberts handed Partick Thistle a 2-1 derby triumph over Queen's Park.
Scottish Cup runners-up Queen of the South cruised past Berwick as doubles from Stewart Kean and Sean O'Connor helped them to a 5-1 away win.
On-loan Ross County striker Craig Gunn netted a 16-minute hat-trick as Peterhead crushed Montrose 6-0.
Kieran Donnelly netted a disputed late penalty to earn Albion Rovers a 1-0 win at Stenhousemuir and two spot-kicks, converted by Sean Kilgannon and Kevin McLeish, saw Forfar come from behind to beat Arbroath 2-1 at Gayfield.
East Fife striker Chris Templeman knocked out former club Brechin with the only goal at Glebe Park and Cowdenbeath won 2-0 at Elgin City.
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