Vicente del Bosque's side needed just a point to confirm a place in the last four yesterday, but they made doubly sure thanks to a fine brace of goals from Jordi Alba and a 62nd-minute header by substitute Fernando Torres.
The world and European champions will now face Italy, who they crushed 4-0 in last year's Euro 2012 final, in the second semi-final in Fortaleza on Thursday, a day after Brazil meet Uruguay in Belo Horizonte.
"We played against a better side, a team who've been together for a long time," said Nigeria coach Stephen Keshi.
"It's a learning process for us, it's good. We have to continue from where we stopped tonight, and build on that."
It was the teams' first meeting since Nigeria beat Spain 3-2 in the group phase of the 1998 World Cup, and if the world champions were out for revenge, they were quick to draw first blood at Estadio Castelao.
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