They are now eager to avoid the mistakes of two years ago, when they finished ahead of England, Argentina and Nigeria in their group only to lose in the next round to Senegal.
The Swedes clinched top spot in Group C and consigned pre-tournament favourites Italy to an early exit when a late goal from Mattias Jonson earned them a 2-2 draw with Denmark.
"I think we've surprised a lot of people by winning the group," said midfielder Fredrik Ljungberg. "We're very happy with that performance."
"Now we want to show we can go further than in the World Cup. We're all looking forward to going on in this competition."
Their reward for Tuesday's gritty performance following a 5-0 victory over Bulgaria and 1-1 draw with Italy will be a quarter-final against Germany, the Netherlands or Latvia.
None of those teams have looked convincing in the group stage and Sweden feel they have a great opportunity to reach the semi-finals, just as they did at the World Cup in 1994.
"Holland and Germany both have good teams but I don't think it matters who we play now," said goalkeeper Andreas Isaksson.
Key to Sweden's progress has been the fighting spirit shown in coming back to claim draws with Italy and the Danes.
Italy in particular outplayed them for the first hour in Porto but Sweden limited the damage to one goal and clinched a late equaliser through the individual brilliance of Zlatan Ibrahimovic.
An even later equaliser from Jonson in the Denmark game brought the 2-2 scoreline that suited both sides and sent Italy home despite their 2-1 win over Bulgaria.
Predictably, it brought accusations from the Italians of a fix but Sweden's co-coach Lars Lagerback underlined how hard his side had had to work to get the result.
"It was a fair fight as anyone could see," Lagerback said. "We always had belief, always had hope, but you never know in this business."
"When you play at this level the opponent is always difficult and I think our performance against Denmark was similar to the Italy game in terms of the way we fought."
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