Erik Hamren's charges looked to be heading for a goalless draw in Friday's first leg in Lisbon, but were consigned to defeat in the 82nd minute as Cristiano Ronaldo stooped to head home Miguel Veloso's pin-point centre, to hand Portugal a slender 1-0 lead.
It means Sweden face an uphill battle to secure their place in Brazil, with a two-goal cushion required at the Friends Arena in Solna to guarantee their progression, although a 1-0 success would lead to extra time and possibly penalties.
The talk before the first encounter between the two sides was largely dominated by which Ballon d'Or candidate, Ibrahimovic or Cristiano Ronaldo, would shine brightest.
However, both players were largely marginalised, until Ronaldo's late intervention.
At 32 years of age, the 2014 World Cup could present Ibrahimovic's last chance to appear at the biggest tournament in world football, and the Paris Saint-Germain forward is confident Sweden can overcome the deficit.
"We've got the measure of them now, and that's an advantage," he said. "It's the last game before the World Cup now. Get behind us and we'll make it."
Hamren is expected to name a similar side to the one that started the first leg, as Sweden look to return to the World Cup after missing out on South Africa 2010.
Portugal's victory was their first over Sweden on home soil, and they will be confident of appearing in their fourth straight finals.
Coach Paulo Bento welcomed Ronaldo and Pepe back to training on Sunday after sitting out Saturday's session as a precaution.
If Portugal do qualify for the tournament it would mark the second consecutive time the play-offs have provided their route, after a 2-0 aggregate victory over Bosnia-Herzegovina in 2009 ensured their place in South Africa.
The last time Portugal defeated their opponents in Sweden came in October 2002 as an 89th-minute strike from Rui Costa ensured a 3-2 friendly triumph.
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