Falkirk striker Zak Rudden, on loan from Rangers, netted a superb hat-trick and Ibrox colleague Glenn Middleton also scored.
Billy Stark’s side had opened their campaign with a deserved 3-1 win against Turkey on Wednesday and easily swept aside the Cypriots yesterday in Rio Ave.
It means the young Scots will face the hosts at Boavista’s stadium in Porto knowing a win will see them reach this summer’s Euro finals in Armenia.
They haven’t qualified since 2006 when they got all the way to the final in Poland, only to lose narrowly to a star-studded Spain team.
Stark has been able to call upon the likes of Chelsea superkid Billy Gilmour, Celtic midfielder Ewan Henderson and Rangers winger Middleton, who would usually have been with the Under-21s, who are in Marbella playing two friendlies.
And Rudden – who also netted against Turkey – helped set up a tantalising last game do-or-die encounter against the Portuguese.