Shapovalov (18th in the world) first beat Thanasi Kokkinakis (95th) 6-2, 6-4 then Auger-Aliassime (6th) brought the point of victory by beating Alex de Minaur (24th) 6-3, 6- 4, under the eyes of Novak Djokovic and his son Stefan.
Canada has come a long way since it was eliminated in March in qualifying by the Netherlands.
To discover
Davis Cup: Schedule and results
But the exclusion of Russia, holders of the title, because of the conflict in Ukraine, left a place: Serbia should have benefited from it, but having previously received an invitation for the final phase 2022, it is Canada which has been fished out.
The Canadians, who had been beaten by Spain in the final in 2019 for the first edition of the new formula of the national team competition, therefore succeed Russia.
Canada finished second in Group B behind Spain in September, before eliminating Germany in the quarter-finals (2-1) and Italy in the semis (2-1).