European champions Spain controlled the match in all phases but were not able to break down Cape Verde, the fifth lowest ranked team in the field at No. 67.
As a consequence the pair delivered the first scoreless draw of this year's event.
The Blue Sharks have goalkeeper Vozinha to largely thank for that. The 40-year-old finished his country's first World Cup match with seven saves.
Spain's first premier chance came in the 39th minute, when Marc Cucurella headed the ball down to Ferran Torres, who clanged the shot off the crossbar. The rebound came to Mikel Oyarzabal's area, but his header was tipped over by Vozinha.
Vozinha had already produced a fine reaction save to deny Torres and then tipped away Aymeric Laporte's glancing header.
Fabian Ruiz had another strong chance to open the scoring with a header in the box in the 56th minute, but directed it right at Vozinha.
Spain waited until the 71st minute to make any subs, when they brought on teenage sensation Lamine Yamal for his first appearance since April 22 due to a hamstring injury.
Yamal caused havoc on the right wing, but even he couldn't get the Spaniards on the scoresheet.
Spain's last great chance came in the 88th minute, when a cross found Oyarzabal open in the box. His first-time shot was deflected by a sliding Pico Lopes out for a corner kick.
Cape Verde earned their first corner kick in the 90th minute and could have stolen a sensational win from it as Diney Borges rose unchallenged, but headed into Unai Simon's arms.
The only time Spain won the World Cup, in 2010, they lost the opening game to Switzerland, so they will not panic.
"You fix things by sticking to the same plan, continuing to improve with more finesse," Spain coach Luis de la Fuente said.
"They are a very organised team. We saw that they sat deep as a unit. It's very difficult to create spaces like that, yet we did create some. We lacked a bit of movement to create more, but when it doesn't want to go in, it doesn't want to go in."
For Cape Verde the knock-out rounds are now conceivable while Uruguay and Saudi Arabia, who meet later on Monday (local time) know qualification will not be easy, even with three teams progressing from the majority of groups.
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