Zlatan joins Paris St Germain - Jean-francois Beausejour
Norway was neck and neck by half time, after goals from Mohammed Abdellaoue and Stefan Johansen equalled Ibrahimovic's first two strikes.
But the lanky Bosnian pulled Sweden ahead in the 57th minute, blasting in a free kick which goal-keeper Rune Jarstein could not keep out. Anders Svensson then hammered in Sweden's fourth goal in the 75th minute.
After the match, the Paris St-Germain star commended Norway for the quality of its game.
"They are a tough team to face. It seems easy when I score three goals, but they were physically strong. And we let them play, so they played good football," he said.