The third smallest nation to compete at the tournament finished as runners-up in Group H behind Spain who beat Uruguay 1-0 in Guadalajara.
The Cape Verde players waited on the field for the game between Spain and Uruguay to end before launching into their celebrations with coach Bubista as well as their fans who were dancing and jumping for joy in the stands.
Cape Verde, who drew all of their group stages matches, will take on defending champions Argentina on 3 July in Miami.
"It's all as if it's a dream," said midfielder Deroy Duarte. "When I was a little boy I dreamed of playing in the World Cup ... it's unthinkable what we've done.
Cape Verde owe a debt to Spain who shut down an unimaginative Uruguay side that ultimately succumbed to indiscipline.
Agustín Canobbio was dismissed in stoppage time for an ugly challenge on Spain defender Pau Cubarsí.
France thrash Norway to win Group I
On Friday afternoon, France walloped Norway 4-1 to claim Group I with a 100 percent record.
Ousmane Dembélé scored three of France's goals to take his 2026 tournament tally up to four goals - the same number as his skipper Kylian Mbappé.
France will take on Sweden in the last 32 while Norway will face Cote d'ivoire in Dallas on 30 June.


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