Striker Teemu Pukki scored from a counter-attack in the 79th minute, his team's first attempt on target after they had withstood waves of attacks from Spain.
Defender Sergio Ramos, wearing the captain's armband on his 100th appearance, had broken the deadlock with a header from a corner just after half-time but Vicente del Bosque's side struggled to make their dominance count.
"We weren't thinking about France because this was the most important game," said the 26-year-old Ramos who became the youngest Spaniard to rack up a century of internationals.
"Now we can think about it," he told Spanish television. "We have a great team in front of us but we can beat them and we have to go with this mentality.
"This result is a shame after celebrating my 100th cap with a goal," added Ramos.
Coach Del Bosque, who passed Ladislao Kubala's record with his 69th match in charge, threw on Pedro for Santi Cazorla at the interval in a bid to pep up the attack and it was Ramos who made the breakthrough.
"We failed to get the shots in to shut out the game with a second goal," said Del Bosque. "They defended from deep very well and what seemed almost impossible happened - they scored.
"We still hold our destiny in our own hands. We have a great team and it is possible to win in France."
