Lowland League leaders East Kilbride caused the shock of the SPFL Trust Trophy third round by thumping hosts Edinburgh City 4-1 as favourites Dundee United also eased through.
Queen of the South and Peterhead also defeated teams from the division above.
But Northern Irish sides Cliftonville and Coleraine were knocked out by Raith Rovers and Hamilton Academical respectively.
Queen's Park eased aside Welsh hosts Bala Town 3-0.
First-half goals from Jack Turner and Barry Hepburn were added to by Ruari Paton in stoppage time.
There was drama before kick-off in Coleraine as a delay to Accies flight from Glasgow meant a later kick-off
However, Lewis Smith gave the visitors the lead after only 11 minutes and, although Lee Lynch equalised, goals from Dario Zanatta and Jamie Barjonas after the break took the visitors through.
Second-half goals from Adam Masson, Lewis Vaughan and Jack Hamilton gave Rovers a convincing win over Cliftonville.
United needed a late equaliser to deny Dunfermline Athletic the three points in last month's Championship meeting, but the hosts were never in danger this time against a side hit badly by injury.
Louis Moult opened the scoring after 18 minutes and an Aaron Comrie own goal and a fine finish from Declan Glass had United heading to a 3-0 victory by half time.
Goals from Nathan Flanagan and Andy McDonald either side of half-time had East Kilbride ahead and, although Gwang Wrad Peter pulled one back for the League 1 hosts before the break, further goals from Ally Roy and Keir Samson secured a convincing victory.
Third-tier Queens knocked out Championship hosts Partick Thistle 3-2.
Craig McGuffie opened the scoring after only seven minutes, the hosts were level through a Steven Lawless penalty soon after, but Gavin Reilly restored the lead before the break.
Ben Stanway levelled again just after half time, but veteran centre-half Efe Ambrose supplied the winner three minutes from time.
League 2 side Peterhead took the lead away to third-tier Annan Athletic through Andrew McCarthy after 15 minutes, with Kieran Shanks adding the second 10 minutes after the break.
Arbroath swept aside Championship rivals Inverness Caledonian Thistle.
David Gold and Tom O'Brien had the hosts ahead and, although Adam Brooks pulled one back just before the break, Arbroath capitalised on Harry Lodovica's 63rd-minute red card to add two more through Scott Stewart and Aaron Steele.
Lewis Hyde scored a late consolation for the visitors.
Lowland League students University of Stirling threatened a surprise as they took an early lead against Airdrieonians through Ciaran McAninch.
Goals within a minute from Josh O'Connor and Rhys McCabe had the Championship side ahead and, although McAninch equalised after the break, Liam McStravick saved the Diamond's blushes with the winner.
League 2 visitors Elgin City also threatened a shock in their first game under new manager Barry Smith as they took an early lead through LiamHarvey, but Championship side Greenock Morton levelled through Robbie Muirhead before the break, with Lewis McGrattan supplying the second-half winner.
Lowland League Albion Rovers took the lead through Niyah Joseph away to East Fife, but second-half goals from Jonathan Page and Connor McManus secured progress for the League 2 hosts.
Second-half goals from Craig Brown and Kane Hester gave Montrose a fine victory away to League 1 rivals Cove Rangers.
League 1 side Kelty Hearts eased through against Dumbarton in a game that both sides ended with 10 men.
Darren Lyon and Botti Biabi gave the visitors a 2-0 lead, Michael Ruth replied before the break for the League 2 hosts, but Biabi added his second before Kelty's Jamie Walker then the Sons' Ryan Wallace were sent off.
The New Saints and Falkirk had already progressed to the fourth round.
The Welsh champions were comfortable 3-0 winners away to Hibernian B on Friday, while the League 1 leaders won 1-0 away to second-tier Ayr United on Wednesday.