Some resolute defending and Teemu Pukki's 79th-minute strike on the counter-attack left Vicente del Bosque's side second in Group I, two points behind France with four games left to play.
Only one team from each group earns direct qualification for the finals in Brazil next year, with the eight best runners-up entering a play-off for the last four European berths.
"Another big slip-up," was the front page headline in sports daily Marca on Saturday, after a second consecutive home draw in qualifying following last October's 1-1 draw with France.
"The World Cup is in danger," read Sport's frontpage, but the message from the team itself was less alarmist.
"We completely dominated for 90 minutes but we didn't have luck in the final third," coach Del Bosque, who guided the team to victory at the 2010 World Cup and at Euro 2012, told a news conference.
"We have been touched by a magic wand in terms of luck in recent years, but we didn't have any today.
"There is no need to be pessimistic because we still hold our destiny in our own hands. We have to go to France and win and after that there are still three more games."
The game resembled last season's Champions League semi-final second leg between Barca and Chelsea, when the English side snatched a draw to progress despite overwhelming possession for the hosts.
"We took a risk with a tactic that is little like cat and mouse and it worked well," Paatelainen said. "We succeeded in frustrating Spain."
The experienced duo were rested for Friday's encounter as they recover from nagging injuries.
"Spain were without Xavi, the hand that rocks the cradle, and Xabi, who provides the framework," sports daily AS wrote on Saturday.
"[Spain's play] needs a degree of precision which wasn't there last night."
"When you don't win you have to know how to handle the criticism. It should make us reflect and react," he told Spanish radio.
"After our goal we eased off a little. We relaxed. It seemed we had done enough."
