Rallied by the support of their home nation, Spain came close to taking the lead on a number of occasions in the first half as they started the game strongly.
A notable chance came after 16 minutes - an early cross from Koke was met by the head of Dani Olmo but the winger was denied by a superb save from Robin Olsson.
Following a mistake from Marcus Danielson, Alvaro Morata was presented with a golden opportunity to find a strongly sought after breakthrough for the Spaniards. However, the striker was unable to compose himself and dragged his effort wide from close range.
The Swedes then came agonisingly close to breaking the deadlock on the stroke of half-time. Alexander Isak's effort was deflected on to the post by Marcos Lllorente following a dangerous counter attack from Janne Andersson's side.
After the one-sided dynamics of the first half, it was Sweden who had the first clear chance of the second - arguably the chance of the match.
Exceptional footwork from Isak allowed him to dance through a sea of Spanish players to drill a low cross towards Marcus Berg at the back post. He sensationally missed the target from point blank range - much to the disbelief of both teams.
As the game went on, Spanish frustrations intensified as Luis Enrique's side were denied two late chances to snatch the three points. Gerard Moreno and Pablo Sarabia squandered crucial chances in the Sweden box with just minutes remaining.
With referee Slavko Vinkic blowing the final whistle in Seville, the valiant Swedes breathed a sigh of relief as Spain were left to rue a host of missed chances as they failed to get off the mark in the Group E.
You can read the full match report on our sister site Football365 here.
What's next for Spain and Sweden?
A hard-earned point for Sweden keeps them in contention for qualification to the knockout rounds. They will travel to St Petersburg to face Slovakia this Friday at the Krestovsky Stadium.