Jon Obika's late goal earned 10-man St Mirren a 1-0 victory over Queen's Park and a place in the Betfred Cup last 16.
Livingston and Dunfermline joined Group A winners Hearts among the second-round seeds while St Johnstone and Ross County also topped their groups following victories.
Ayr also progressed as group winners thanks to a penalty shoot-out success over Stranraer.
Dundee United joined Kilmarnock and Hamilton in being eliminated after wins for Alloa and Arbroath saw them finish among the four best runners-up along with Falkirk.
Hibernian and Dundee both saw their qualifications confirmed before they face each other at Easter Road on Sunday but a place among the seeds is on offer for the winners.
St Mirren endured some anxious moments at Hampden before booking their place in the second round.
Joe Shaughnessy was sent off for the second time this season when he put in a poor challenge on Michael Doyle in the 49th minute at Hampden.
Bob McHugh saw a close-range header saved for the Spiders before Obika headed home Kyle McAllister's corner nine minutes before the end.
Partick Thistle and Morton had hopes of overtaking the Buddies but they drew 0-0 with the Jags taking the bonus point.
St Johnstone came through their winner-takes-all clash at Peterhead with the help of two second-half Stevie May penalties which the striker both won himself.
Chris Kane added to the visitors' lead in the 77th minute before Shaun Rooney's own goal made the final score 3-1.
Dundee United finished above Peterhead in second place in Group C but eight points proved insufficient to qualify.
Ross County comfortably secured their passage with a 3-0 home win over Stirling in front of 300 fans.
Oli Shaw, Ross Stewart, from the penalty spot, and Regan Charles-Cook were on target as County finished on 11 points.
Arbroath's home game against Elgin was held up by 25 minutes following a pre-match injury for an assistant referee but the hosts secured their passage as runners-up to County as a David Gold double and Scott Stewart strike earned a 3-0 win.
Dunfermline left it late to secure their fourth win out of four after trailing Clyde 2-0 going into the final half hour.
Kevin O'Hara pulled one back from the spot, Declan McManus levelled in the 87th minute and Paul Watson headed a stoppage-time winner as the Pars finished three points above Falkirk.
Ayr and Stranraer were playing off for Group F top spot and Darryl Duffy missed a penalty soon after giving the League Two side an early lead. Ayr's Luke McCowan levelled two minutes after the break and his side won 6-5 on penalties.
Livingston beat Airdrie 4-1 to complete a perfect record in Group H. Alan Forrest and Jay Emmanuel-Thomas both hit doubles following a goalless first half with Thomas Robert on target for the visitors.
Alloa sealed progress as runners-up after coming from two goals down to beat Stenhousemuir 4-2. Liam Buchanan netted the first goal of his hat-trick in the 64th minute and Steven Hetherington scored in the closing stages.
In Group A, Raith and Inverness recorded 1-0 wins over Cowdenbeath and East Fife respectively but neither side joined Hearts in the second round.
Hamilton's Lanarkshire derby with Albion Rovers was postponed after the League Two side reported three positive Covid-19 tests.
Eamonn Brophy and Mitch Pinnock were on target as Kilmarnock beat Dumbarton 2-0 at Rugby Park.
In other meaningless games, Cove Rangers beat Forfar 1-0 and Kelty Hearts won 2-0 at Brechin.
