Sergio Ramos gave Vicente Del Bosque's side the lead shortly into the second half but Teemu Pukki made the most of a rare chance for the visitors to draw level on 78 minutes.
The result means the World Cup holders slipped to second place in Group I and need to beat leaders France in Paris next Tuesday if they are to reclaim their place at the top of the group.
Spain were the far superior side throughout the match but Finland had a clear strategy - allow their opponents almost exclusive ownership of the ball whilst making sure they allowed them minimal space in the final third - which they stuck to perfectly.
Their tactic paid off in the first half, limiting their opponents to taking shots from outside the area as they were unable to break down the Finnish defence and create a clear effort of their own through their slick, short passing.
Cesc Fabregas, Andres Iniesta and Santi Cazorla all saw efforts from outside the area miss the target, while the clearest chance fell to the Arsenal midfielder, who later shot high over the bar after pouncing on a loose ball.
For all Spain's possession, Finland goalkeeper Nikki Maenpaa only needed to make one proper save in the opening 45 minutes, pushing away an effort from Iniesta.
Del Bosque made one change at the break, taking off Cazorla and bringing on Pedro, but when Spain broke the deadlock on 49 minutes, it had little to do with the substitution.
David Silva sent in a corner and Ramos, making his 100th appearance for Spain and wearing the captain's armband to mark the occasion, rose to head the ball beyond Maenpaa and into the bottom corner.
The Real Madrid centre back, playing almost in a central midfield role due to Spain's high defensive line, then came close to doubling the advantage but saw his shot from the edge of the area fizz narrowly wide of the left-hand post.
Although Spain did not create any clear-cut chances that would have seen them increase their lead, they were always in control and a home victory never looked in doubt - until they got their biggest shock of this World Cup qualifying campaign so far and found themselves level with 12 minutes to go.
Finland broke down the left hand side, Tim Sparv delivered a low cross into Pukki who was unmarked just outside the six-yard box, and the striker, who spent a year in Spain with Sevilla, shot past Victor Valdes to equalise.
It was the visitors' first shot on target and only their fourth attempt of the evening.
Spain laid siege to the Finland goal in the closing minutes.
Substitute Alvaro Negredo missed two great chances to restore his side's lead, first heading the ball just wide of the near post from a few yards out.
Then he failed to make enough contact with a cross, allowing Maenpaa to gather, but as he went to ground without the ball in full control Silva tried to take it off him, and an angry confrontation between both sides ensued, Silva booked for his involvement. Ramos had another opportunity to score late on but sent his shot over the bar, while Mata was also unable to hit the target with his effort.
When the final whistle sounded the Finnish players went wild, celebrating a historic result which saw their country, who have never qualified for a European Championship or a World Cup in their history, hold the holders of both tournaments to a draw away from home.