The AGF Aarhus midfielder scored the only goal of the game from long range 12 minutes from time, with goalkeeper Andreas Isaksson partly at fault.
The visitors had two second-half strikes disallowed and were unable to capitalise on their dominance after the break, with Zlatan Ibrahimovic a central figure.
Sweden are still in with a shout of the play-offs, a point behind Portugal with one game remaining.
Their rivals for second spot triumphed 3-0 against Hungary tonight but saw Cristiano Ronaldo limp off in the 25th minute tonight - meaning the Real Madrid star will surely be a major doubt for Wednesday's crunch qualifier against Malta.
Hungary were level on points with Portugal going into the game at the Estadio da Luz, but two goals from Simao either side of Liedson's header have left the visitors needing a small miracle to qualify.