Gary Mackay-Steven and Liam Boyce were on target as Hearts won 2-0 at Peterhead, while Livingston triumphed 3-0 at Brechin.
Morton earlier became the third team to forfeit their opening group game after "multiple" players tested positive for Covid.
Stranraer were awarded a 3-0 win to join Forfar and St Mirren in being handed three points following coronavirus issues at Ross County and Dumbarton respectively.
Mackay-Steven kick-started Hearts' season in the 31st minute at Balmoor when he cut in from the left and fired home.
Boyce swept home a cross from Northern Ireland team-mate Michael Smith just before the hour mark and both goalscorers had several other chances.
Elsewhere in Group A, there was a surprise as Cove Rangers fell to a 3-2 home defeat by Stirling following some late drama.
Cove fought back from two goals thanks to Fraser Fyvie's late double, but Nathan Flanagan broke clear four minutes into stoppage-time to net his second goal of the game.
Tom Parkes and Ayo Obileye hit debut goals as Livingston won at Glebe Park.
Former Exeter defender Parkes scored with his first touch for the club inside a minute as he converted a corner from close range. Obileye also netted from a corner, heading home Josh Mullin's delivery just after the hour mark.
Bruce Anderson was twice denied a debut goal by the Brechin goalkeeper and his replacement, Jack Hamilton, squandered some late chances before Jackson Longridge stabbed home Alan Forrest's low cross in injury-time.
Raith join Livi on three points in Group D after Lewis Vaughan's 21st-minute goal was enough to edge a Fife derby at Cowdenbeath.
Kilmarnock started their season with three points as second-half strikes from Fraser Murray and Jason Naismith earned Tommy Wright's side a 2-0 win at East Kilbride.
Dunfermline joined St Mirren on three points in Group H after a clinical 4-2 victory over Partick Thistle at Firhill.
Brian Graham fired the Jags ahead in the 16th minute, but three goals in 13 minutes from Nikolay Todorov, Aaron Comrie and Kyle MacDonald put the visitors in command.
Todorov chipped the goalkeeper early in second half before Zak Rudden headed one back.
Calum Biggar's first goal for Queen's Park earned the Spiders a 1-0 win at Palmerston against Queen of the South, who hit a post through Ruben Soares-Junior.
Elsewhere in Group F, which also includes Motherwell, Airdrie salvaged a 1-1 draw against Annan in stoppage-time when Matthew MacDonald cancelled out Tony Wallace's opener. Annan claimed the bonus point on penalties.
Ayr lost a penalty shoot-out against Albion Rovers after a goalless draw at Cliftonhill.
Arbroath joined Dundee United on three points in Group B after Luke Donnelly headed the only goal at Elgin with 10 minutes left.
Montrose joined Forfar at the top of Group C after beating Highland League champions Brora 3-0 thanks to goals from Martin Rennie and Blair Lyons plus a Lewis Milne penalty.