Spain booked their place at Euro 2024 with a win in Norway on Sunday, also helping Scotland qualify from Group A.
Barcelona midfielder Gavi scored early in the second half to help the 2008 and 2012 European champions progress with two games to spare.
Erling Haaland's Norway, who last appeared at a major tournament in Euro 2000, can now only potentially qualify through play-offs.
They are now relying on their Nations League rankings to make it.
Spain barely allowed Manchester City striker Haaland a sniff all night long on a frustrating night for Norway, who sit five points behind their opponents and Scotland with only one match remaining.
La Roja thought they had taken the lead after 20 minutes when Stefan Strandberg diverted the ball towards his own net and Alvaro Morata hammered home from almost on the goal line.
The goal was ruled out for offside against Morata. Dani Carvajal's lofted ball forward was aimed at Brighton winger Ansu Fati before Strandberg's intervention, and Morata had left the ball it would have been an own goal.
Gavi eventually fired Spain ahead in the 49th minute after a hectic scramble in Norway's area, pouncing when Mikel Oyarzabal's shot was deflected into his path.
It was the 19-year-old's fifth goal for his country in 25 appearances.
Arsenal captain Martin Odegaard sliced an effort wide at the other end as the hosts made a rare foray forward, and Spain goalkeeper Unai Simon saved comfortably from bright teenager Antonio Nusa.
A flat Norway could not muster danger during eight minutes of added time, apparently resigned to their fate, while Spain broke into celebrations at the final whistle.
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