The Premiership pair – who defeated Kelty and Stenhousemuir respectively in their final first round matches – will progress to the knockout phase along with section winners Partick, Inverness, Ross County, Falkirk, Dundee, Arbroath and Annan.
Queen of the South – despite notching a relatively modest eight points – are on course to qualify as one of the three best runners-up as long as Raith Rovers do not win away to Aberdeen on Sunday.
Results on Saturday mean the Dons are assured of a place in the next round even if they lose at Pittodrie.
Killie’s 4-1 home win over Stenny saw them finish as the best second-placed team on 10 points, with Oli Shaw bagging a double for Derek McInnes’ side. In the other game in Group B, table-toppers Partick enjoyed a similarly comfortable 4-2 home victory over Montrose.
Livingston knew they needed results to go their way in order to qualify but they stuck to their side of the bargain by defeating Kelty 2-0 through goals from Sean Kelly and Phillip Cancar.
Inverness secured top spot in Group G after drawing 1-1 at home to Cove Rangers and then winning the penalty shootout.
Ross County were the most impressive performers of the day as they roared into the last 16 with an emphatic 7-0 home win over East Fife, with summer signings Owura Edwards and Kazeem Olaigbe both netting doubles.
In the other game in Group C, Dunfermline missed the chance to finish as one of the three best runners-up when they were held to a 1-1 draw by Alloa before losing on penalties.
Arbroath sealed top spot in Group E with a 3-0 victory at home to second-placed Airdrie.
The Diamonds, who travelled to Gayfield with a chance of qualifying themselves, were blown away by goals from Michael McKenna, Kieran Shanks and Jason Thomson.
In the other game in the section, Premiership side St Mirren – who were already eliminated – claimed some form of consolation as they finished up with a 3-1 home win over FC Edinburgh, with new signings Mark O’Hara and Jonah Ayunga, who bagged a brace, on target.
In Group F, with runaway winners Annan idle, Queen of the South won the race to finish second as they defeated Elgin 2-0 at Borough Briggs and – with results elsewhere going their way – they now need one more favour from Aberdeen on Sunday.
There was no such luck for Premiership side St Johnstone who finished below Queens on goal difference and crashed out despite beating Ayr 1-0 at home through a Graham Carey goal.
Alex Jakubiak scored an early double as Dundee tied up top spot in Group H with a 5-1 home win over Forfar, while Hamilton blew the opportunity to finish as one of the best runners-up after conceding a 78th-minute equaliser at home to Queen’s Park.
Falkirk secured top spot in Group D with a 1-0 home win over Clyde, while Morton defeated 10-man Bonnyrigg 3-1 to jump above Hibernian and finish second.
In Group E – where Stirling won 3-0 at home to Peterhead – Raith will attempt to pull off an upset away to Aberdeen on Sunday and follow the table-topping Dons into the next phase.