Ryan Christie earned his 26th senior cap for Scotland as they secured a seeded spot in the World Cup play-off semi-finals after triumphing 2-0 against Group F leaders Denmark on Monday.
The Scots had already guaranteed second place and needed at least a point against the previously-unbeaten Danes to give themselves a chance of a home draw.
And goals either side of half-time from John Souttar and Che Adams saw the Hampden Park hosts take a step closer to qualifying for a first World Cup finals since 1998.
Christie, who sat out their 2-0 win against Moldova on Friday due to suspension, was restored to the starting line-up by head coach Steve Clarke.
The winger almost played a part in Scotland taking the lead midway through the first half when he provided the assist for Adams whose effort was superbly saved by Kasper Schmeichel.
Souttar drew first blood when he headed home in the 35th minute, the Hearts defender celebrating his first Scotland game since being sent off in a 2018 defeat by Israel.
And after Christie had been replaced by Stuart Armstrong in the 80th minute, Southampton striker Adams burst clear to seal victory four minutes from time.
His breakaway goal secured a sixth competitive victory in succession for the first time since winning six Home Nations matches in a row between March 1928 and February 1930.
Goalkeeper Mark Travers was an unused substitute as Republic of Ireland concluded their Group A qualifying campaign with a 3-0 win against Luxembourg in the Stade de Luxembourg on Sunday.
Second-half goals from Shane Duffy, Chiedozie Ogbene and Callum Robinson ensured the Boys in Green would finish third, above Luxembourg on goal difference.
Cherries academy goalkeeper Ollie Camis started as Wales went down 2-0 against Portugal in their second 2022 Under-17 European Championship qualifier in the Algarve on Saturday.
Diogo Monteiro’s 18th-minute goal was added to by Rodrigo Ribeiro four minutes from time as Portugal followed up their 5-0 victory over Kazakhstan on Wednesday.
Camis will be hoping to keep his place as Wales bid to join Portugal in the next phase of qualifying when they meet Kazakhstan in Albufeira on Tuesday (3pm).
Chris Mepham, Orjan Nyland and Jefferson Lerma will also be hoping to feature for their respective countries when World Cup qualifying continues across the globe on Tuesday.
Mepham’s Wales will be looking to secure second spot in Group E when they host leaders Belgium at the Cardiff City Stadium (7.45pm).
Goalkeeper Nyland will be hoping to help Norway progress when they face Group G leaders Netherlands in Rotterdam (7.45pm), while Lerma’s Colombia entertain Paraguay in Barranquilla (11pm).
Midfielder Gavin Kilkenny will be keen for some game time when Republic of Ireland host Group F leaders Sweden in a 2023 Under-21 European Championship qualifier at the Tallaght Stadium in Dublin (7pm).
