The yellow-clad had to sweat from the start in the 30-degree heat in Seville.
Spain rolled the ball in the Spanish manner and Sweden kept its promise and "ran out of just hell", as national team captain Janne Andersson promised before the match.
Spain also had several qualified chances, but those times the finishes kept sufficient quality so Robin Olsen nailed again in the goal.
A Swedish miss in the Swedish defense by Danielson in the first half gave Alvaro Morata a free kick against Olsen, but the finish went outside.
Alexander Isak impressed
But Sweden was not without a chance either.
And the times Sweden could threaten, there was usually a common denominator: Alexander Isak.
The 21-year-old showed proof of both power and technique and gave the Spanish midfielders a tough match.
In the first half, he had a finish that was controlled in the post by a defender.
In the second half, after an impressive action, he was able to free Marcus Berg.
Unfortunately for the Swedish part, the ball bounced unfortunate for Berg who did not get a finish.
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Isak had super position - took the post
Olsen with giant rescue in the 90s
The last 30 minutes were a battle against the clock for Sweden, who just tried to persevere.
In the 90th minute, Robin Olsen again stood for a huge save when Moreno thought he had nodded home three points to Spain.
Sweden held on and persevered - and fixed a point in the pre-tough opening match against Spain.
0-0 and a dream result for Sweden in the group.
Now Slovakia is waiting for Sweden on Friday.
Slovakia who, somewhat unexpectedly, defeated Poland 2-1 earlier on Monday night.
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Giant rescue by Olsen