The Milan forward scored the first and made the second for England’s Group D rivals, with Ola Toivonen and Christian Wilhelmsson also getting on the score sheet.
Iceland kept themselves in it thanks to headed efforts by Kolbeinn Sigthorsson and Hallgrimur Jonasson, but could not overcome the gulf in class between the two.
Sweden imposed themselves on their rivals immediately with Sebastian Larsson setting up Ibrahimovic within 37 seconds of the whistle. Thankfully for Iceland, Jonasson was on hand to block the shot.
There was no denying the hosts a minute later though, Larsson again the architect from the right as he crossed high for Ibrahimovic. The lanky Milan striker’s finish was not clean, but a devilish bounce was enough to evade goalkeeper Hannes Thor Halldorsson and put the home side in front.
Spurred on by his 30th international goal, Ibrahimovic turned provider 13 minutes later as he shook off his marker with a cheeky sidestep and rolled the ball low and across goal for Toivonen to prod home a second from a yard out.
The doubling of the lead was the catalyst for the hosts to take their feet off the gas; Kim Kallstrom’s impact diminished when his side did not dominate possession while full-backs Behrang Safari and Andreas Granqvist looked particularly exposed due to the forward runs of their own team-mates.
This brought joy for Rurik Gislason and Ari Freyr Skulason, although time after time their crosses were rendered useless due to a lack of support.
The exception came after half an hour when Skulason’s cross from the left touchline was deftly glanced home by Ajax youngster Sigthorsson, who continued to enhance his growing reputation by adding to the goal he netted against France at the weekend.
Widespread substitutions in the second half did their usual job of disrupting any flow that the game had built up, the departures of the influential Kallstrom and Ibrahimovic in particular creating a void that Pontus Wernbloom and Wilhelmsson were largely incapable of filling.
The exception came 13 minutes from time when a poor clearance from Halldorsson was charged down by Toivonen. He then unleashed a delicious chip to find Wilhelmsson, the substitute restoring Sweden’s two-goal advantage with a sweet half-volley.
Emir Bajrami, who replaced Larsson at the break, had three chances himself – all on his unfavoured left foot – but forced an excellent save from Halldorsson with three minutes to go as the Icelandic keeper tipped his shot onto the bar.
Iceland, who seemed to suffer more by their substitutions than their rivals, kept pushing on and pulled another back with the last touch of the game; Jonasson heading home from a corner to make it a pair of 3-2 defeats in four days.
The performance of Toivonen and Markus Rosenberg, meanwhile, gives Sweden coach Erik Hamren a selection headache for their next friendly against Serbia on Saturday and their Euro 2012 opener against Ukraine a week later.
With Manchester City starlet John Guidetti left out of the Euro squad and Johan Elmander still struggling with his fitness, both men now have a great opportunity to start when the tournament begins.