The Bairns leapfrogged their new Championship rivals thanks to first-half goals from Joe McKee and Nathan Austin.
McKee converted an Alex Harris cutback in the 21st minute and Austin cut inside and fired home two minutes before the break. Robbie Thomson saved well from George Oakley but Falkirk finished strongly with Austin and McKee both threatening to add to their tallies.
Stirling eased to a 3-1 victory over Forfar with two goals from Callum Morrison and one from Ross Kavanagh, with Mark Miller’s late header of little consolation to the Loons.
Livingston took a big step towards qualifying after a 2-0 win over Airdrie kept them four points clear of Partick Thistle in Group H.
Dylan Mackin stabbed home Craig Halkett’s cross against his former club in the 21st minute and the latter netted himself when he headed home seven minutes after half-time.
Dunfermline stayed top of Group B ahead of Hearts as they made it eight points from three games with a 5-1 win over Peterhead. Declan McManus and Joe Cardle both hit doubles at East End Park, Rory McAllister pulled one back from the spot before Scott Ross put through his own net.
Arbroath moved above Hibernian into second place in Group D thanks to a 4-0 derby win over Montrose. David Gold drilled them ahead at Gayfield after half an hour with a crisp finish and Danny Denholm added a second-half double before Steven Doris netted in injury time.
League Two Clyde claimed a surprise 2-1 win over Championship opponents Dumbarton at Broadwood to move on to six points in Group E alongside Ayr and Kilmarnock. Craig Barr had given the Sons a half-time lead after he scrambled home from a corner but Darren Miller levelled with a clever lobbed finish from an acute angle before Max Wright headed home the winner.
Connor Shields got his first senior hat-trick as Albion Rovers beat East Kilbride 5-2 at K-Park to move level on four points with Hamilton in Group G ahead of Tuesday’s Lanarkshire derby at Cliftonhill. The visitors raced into an early two-goal lead through Alan Trouten and Gary Fisher and Shields notched twice after the break. The Lowland League champions pulled two goals back in two minutes from Sean Winter and a Michael McMullin own goal, before Shields secured the match ball.
Elsewhere, Queen’s Park were too strong for Edinburgh City in their 3-0 win at Hampden thanks to goals from Dominic Doherty, a Chris McKee own goal and Anton Brady.