The Paris Saint-Germain frontman's fourth goal was particularly special - a 30-yard overhead kick that will be remembered for many years.
Here, Sports Mole analyses the action in the Swedish capital.
On target 9
On target 7
Was the result fair?
Hmmm. For the most part England were fairly comfortable but ended up being undone by some clever finishing from Ibrahimovic. The first 20 minutes were fairly mundane but after that it was a great game to watch.
Fairly timid but inspired by their world-class number 10. They looked especially iffy defending set pieces but will always manage to score goals as long as Ibrahimovic is up there.
Pretty good. Debutants Leon Osman and Caulker were impressive on their international bows while Sterling also did okay. Steven Gerrard will be disappointed not to have won on his 100th appearance for the Three Lions and Joe Hart will be particularly disappointed with what may have been his worst performance for his country. All four of the Swedish goals were down to errors from the visitors and Hodgson will be particularly angry with that.
Sports Mole's man of the match
Zlatan Ibrahimovic: The award was heading for Osman until Ibrahimovic's late antics. You can't not give MOTM to a man who scores four goals. His finish for the first was a clever toe-poke but although he struck the second and third well, Hart will feel he should have kept both out. As for the fourth, well, we'll be seeing that one for years to come.
There were no really bad gaffes but this award goes to Hart for letting in Ibrahimovic's free kick on his side of the goal. Tom Cleverley almost got it for his miss in the opening half from about six yards out.
Svein Oddvar Moen had a solid game but there was one strange moment where he booked Jack Wilshere for a cynical challenge on Ibrahimovic and then moments later didn't book the PSG man for a similar challenge on the Arsenal midfielder.
Sweden: Next up for the Swedes at the brand spanking new Friends Arena is a visit from Argentina and the world's best player, Lionel Messi, in February.
England: England also face a South American giant when Brazil come to Wembley in the second month of 2013.