The tiny island nation off the west coast of Africa, making their debut on soccer's grandest stage, qualified on Friday with a third straight World Cup draw.
They had already held 2010 champions Spain to a 0-0 draw and then came from behind to get a 2-2 result against Uruguay.
The win put the team into second place behind Spain, who beat Uruguay 1-0 to win the group.
The Cape Verdeans will now meet reigning World Cup champions Argentina in Miami on July 3.
On the eve of the match, Cape Verde coach Bubista mused, "everyone is entitled to dream and nothing is impossible."
The Blue Sharks proved him right, overcoming seemingly insurmountable odds as this country of just more than 500,000 reached the round of 32.
A woman, her face painted with a flag of the archipelago, held a sign that read: "Small Islands, Big Dreams."
A dream that these underdogs have made reality as they continue their charmed run on the world stage.
They did it with another strong game from Vozinha, the 40-year-old goalkeeper whose tournament success has helped him amass more than 16 million Instagram followers.
He made a save in first-half stoppage time, grabbing a header from Mohamed Kanno to keep Saudi Arabia scoreless. He then produced another in the 66th minute when he leaped to deflect a shot from Mohammed Abu Al-Shamat.
In the 92nd minute, Vozinha stopped a shot by Abdullah Al-Hamdan. A group of shirtless men in the crowd each painted one letter of his name on their chests as they cheered Cape Verde.
But Vozinha had a much bigger fan among the crowd of 68,278 as his mother Ana Candida Evora watched from a luxury suite, waving a tiny Cape Verde flag. It was her second match of the tournament after missing Vozinha's epic seven-save performance against Spain because of visa issues.
Cape Verde had a chance to score in the 50th minute, but Kevin Pina's shot from distance soared above the crossbar. Another chance came in the 74th minute when Laros Duarte's shot from the middle of the box was stopped by goalkeeper Mohammed Al-Owais.
A last chance to score came in the final seconds when Nuno da Costa sent a shot from the middle of the box wide left.
But it didn't matter because a couple of minutes after the final whistle, Spain completed their victory over Uruguay to set off a joyous celebration among Cape Verde's players and fans.
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