Cristiano Ronaldo scored the only goal of the first leg in Lisbon, putting the Seleccao in position to clinch a World Cup berth with a draw in Solna.
Erik Hamren's charges looked set to claim 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 pinpoint center and hand the Seleccao a 1-0 lead.
It means Sweden faces an uphill battle to secure its place in Brazil, with a two-goal cushion required at the Friends Arena in Solna to guarantee progression.
The talk before the first encounter was largely dominated by which Ballon d'Or candidate, Ibrahimovic or Ronaldo, would shine brightest. However, both players were largely marginalized until Ronaldo's late intervention.
At 32, the 2014 World Cup could present Ibrahimovic's last chance to appear at the biggest tournament in soccer and the Paris Saint-Germain forward is confident Sweden can overcome the deficit if the fans really get behind them.
"We've got the measure of them now, and that's an advantage," the forward 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 looks to return to the the game's grandest stage after missing out on South Africa 2010.
Friday's victory was Portugal's first over Sweden on home soil and it will be confident of appearing in its fourth straight finals. Coach Paulo Bento welcomed Ronaldo and Pepe back to training Sunday after they sat out Saturday's session as a precaution.
If Portugal does qualify for the tournament, it would mark the second consecutive time the playoffs have provided its route, after a 2-0 aggregate victory over Bosnia-Herzegovina in 2009 ensured its place in South Africa.
The last time Portugal won at Sweden came in October 2002 as an 89th-minute strike from Rui Costa gave it a 3-2 friendly win.