Blue-yellow took a magnificent victory after goals from Alexander Isak and Viktor Claesson.
With the achievement, Sweden, which now leads the World Cup qualifying group with two points more than Spain and one match less played, has a perfect position for the five remaining matches.
However, Sweden got off to a nightmare start.
The Swedish defense ended up on their hind legs and Jordi Alba was able to serve Carlos Soler to 1-0 for Spain.
Uphill for Sweden directly.
But the reply came immediately.
Alexander Isak had the ball glued to his feet and got the chance to fire from a distance - and he did.
The Real Sociedad striker's finish was distinct and looked in behind Spanish goalkeeper Unai Simon.
A crackling start to the World Cup qualifier.
A first half where Sweden stood up well.
- Clearly positive.
The changes have felt sharp, especially with Isak and Kulusevski.
It feels dangerous then.
In the end, I think you can manage to nurture the ball, which is very positive to see, said SVT Sports expert Daniel Nannskog at half time.
Viktor Claesson match hero
Spain was close to getting the same good start in the second half as the first.
But the Swedish goalkeeper Robin Olsen closed the door that time.
A tight situation led to him getting a shot on him and the Swede reacted quickly and stopped the finish.
A few minutes later, more precisely in the 57th minute, it was instead Sweden's turn.
Dejan Kulusevski appeared on cue near the post, and steered it past the goalie.
If Spain lost motivation?
No.
Adama Traore turned, twisted and made Emil Forsberg slide along the lawn and then pulled with a heavy shot - but a new sharp save by Olsen kept Sweden in the lead.
Now a training match against Uzbekistan awaits on Sunday, at 15.00, for Sweden.