"Ibra" capped an great personal display with a breathtaking 25-metre injury-time overhead-kick from a botched Joe Hart header as Sweden avenged their 3-2 defeat by England at Euro 2012.
In doing so he spoiled the celebrations of England captain Steven Gerrard, who became the sixth man to win 100 caps for his country.
"It's not often you score four goals against such good opposition," the striker told a news conference.
Gerrard was the first to praise the Swede, who moved into third place in his country's all-time scoring chart taking his tally to 39 goals from 85 internationals.
"His performance tonight was simply world class and that fourth goal was one of the best I've ever seen," Gerrard told ITV.
"I thought we were very comfortable till we started making all those changes.
"I'm going to give my shirt to my dad - he has supported me all through my career and he deserves to have it."
England coach Roy Hodgson was pleased with his inexperienced side's performance but was left stunned by Ibrahimovic.
"The fourth goal was the crowning glory [but] I'd have rather seen it against someone else," he said.
Sweden coach Erik Hamren also waxed lyrical about his captain's ability as his side got off to a winning start in their new home.
"We have a world star who scores four goals," he said.
"The last one? You might never see that again in your life. Unbelievable, really."
Ibrahimovic scored the first goal at Sweden's new home when he fired home after 20 minutes at the second attempt from Martin Olsson's cross after Steven Caulker, one of six England debutants, blocked his first shot.
The ball ran kindly to the Swede who lashed it into the roof of Hart's net.
Three minutes later Gerrard created England's second when defender Caulker got on the end of his captain's free-kick for a debut goal.
Roy Hodgson handed six players their international debuts but Gerrard's experience was much-needed in central midfield and he had a good match, going close to a goal on two occasions.
His equaliser came as he chested down Anders Svensson's pass to fire past Hart and minutes later his thunderous free-kick was deflected past the Manchester City goalkeeper to put Sweden 3-2 up.
Hart's misery was complete a minute into stoppage time as his header was spectacularly volleyed into the unguarded net by Ibrahimovic from outside the box to cap a man-of-the-match performance as Sweden scored three in the last 13 minutes.
As well as Caulker, Hodgson gave first caps to starters Leon Osman and 17-year-old Raheem Sterling, who became England's fifth youngest player of all time.
"I thought for 75 minutes we played very well when we had the more experienced players on the pitch," Hodgson said.
