The islands, who did not even bother with international competition a decade ago because results were so poor, caused another upset at the weekend with a 2-0 win in Tunisia wrestling away top spot in their group from the fancied north Africans.
Cape Verde also eliminated Cameroon in the African Nations Cup qualifiers before going on to reach the quarter-finals of the event in South Africa at the start of this year in their debut at a major tournament.
The former Portuguese colony is now in line to be seeded when FIFA conducts next Monday's draw for the five play-off matches that will determine which African countries go to next year's World Cup in Brazil.
It is expected Ivory Coast, Ghana, Algeria, Nigeria and Cape Verde will be placed in one pot while Burkina Faso, Cameroon, Egypt, Senegal and Ethiopia go in another.
The play-offs will be played over two legs in October and November.
If Cape Verde make it to Brazil they will become the smallest country to compete at a World Cup finals.
The population of the islands is just under half a million, fewer than that of Trinidad and Tobago who qualified for the 2006 edition in Germany.
Cape Verde coach Lucio Antunes, a part-time air traffic controller, spent several weeks understudying Jose Mourinho at Real Madrid last year and delighted reporters when he burst into song at a news conference during the Nations Cup in January.
Antunes's players are drawn from emigrant communities across Europe, including France, Portugal and Netherlands, and use Brazilian-style nicknames like Fock, Platini and Stopira.
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- Cape Verde