Sebastian Larsson snapped up a loose pass in midfield before releasing his captain with a perfectly-weighted through ball, which Ibrahimovic coolly slotted home low to goalkeeper Rune Jarstein's right in the second minute.
The tall striker netted his second just before the half-hour mark, latching on to Albin Ekdahl's inch-perfect pass and finishing into the same corner of the net.
Norway pulled a goal back when Mohammed Abdellaoue fired home a penalty in the 38th minute and Stefan Johansen's shot deflected off Mikael Antonsson into the net to level the scores.
Ibrahimovic completed his hat-trick in the 57th minute, blasting in a free kick from a central position which Jarstein could not keep out.
Substitute Anders Svensson scored the goal of the night in the 75th minute, hammering home a twisting, dipping shot for Sweden's fourth on his 142nd international appearance.
(Reporting by Philip O'Connor, editing by Ed Osmond)