Top-flight Dundee began their Scottish League Cup campaign by hammering League Two Stirling Albion 4-0 in Group D.
Fourth-tier Peterhead earned two points with a penalty shootout win over League One Brechin City after their match finished goalless.
In Group C, Inverness of the Championship cruised to a 2-0 victory over Highland League Cove Rangers.
And League Two Cowdenbeath beat Fife counterparts Raith Rovers, a league above them, by the same scoreline.
At Forthbank, Sofien Moussa scored in either half as Neil McCann's Premiership visitors eased past the Binos.
The Tunisian striker set up new signing Jean Alassane Mendy to net Dundee's third on his competitive debut.
Craig Wighton added a fourth.
Defender Jason Brown scored the decisive penalty at Glebe Park, with Peterhead prevailing 5-4 in the shootout against Brechin, who were relegated from the Championship last season.
Dunfermline Athletic did not play on Saturday, and get their season and Group D campaign under way when Peterhead visit East End Park on Tuesday night.
Meanwhile, Nathan Austin scored two first-half goals as John Robertson's Inverness earned a comfortable victory at the Caledonian Stadium.
The striker twice converted from close range when George Oakley, then Liam Polworth, picked him out.
A Jordyn Sheerin double earned Cowdenbeath all three points against Raith Rovers at Stark's Park.
Heart of Midlothian, the Premiership team in Group C, do not play until Wednesday, when they make the trip to Cove Rangers.
Hearts boss Craig Levein watched Cove's defeat from the stand in Inverness while his team continued their pre-season preparations with a 5-1 friendly win over League Two Forfar Athletic.
Inverness CT 2-0 Cove Rangers
Raith Rovers 0-2 Cowdenbeath
Stirling Albion 0-4 Dundee
Brechin City 0-0 Peterhead (Peterhead win 5-4 on pens)