In the first two games of this competition, Ibrahimovic and his teammates have mustered a grand total of zero shots on target.
After a fortuitous own goal salvaged an impotent Sweden team a draw against the Republic of Ireland, coach Erik Hamren opted to add another striker, John Guidetti, to his starting XI in a bid to add some much needed firepower for Friday's game against Italy.
But with just one international goal to his name, the former Manchester City striker was unable to provide any attacking impetus, as Italy qualified for the last 16 thanks to Eder's late goal.
In a drab first half, the biggest talking point came when Ibrahimovic clashed with defender Andrea Barzagli in the penalty area.
The 34-year-old went down holding his ankle, but Hungarian referee Viktor Kassai awarded a free kick in Italy's favor.
Within 60 seconds of the restart, Guidetti went down theatrically holding his face after a clash with Giorgio Chiellini, but Kassai was unmoved, with replays showing it was merely a clash of shoulders.
In truth, Sweden's service to Ibrahimovic has been poor throughout the tournament, though finally a Martin Olsson cross found its way to Sweden's captain at the far post.
It looked easier to score than miss, but the 34-year-old Ibrahimovic somehow contrived to spoon the ball over the crossbar from all of two yards -- thankfully for him, the linesman flagged for offside to spare his blushes.
With the game seemingly petering out into a draw, Italy finally found a spark with just two minutes of regulation time remaining.
Chiellini's long throw was headed on by Simone Zaza and gathered by Eder, who jinked inside, gliding past three Swedish defenders before lashing a shot into the net.
Soon afterwards, Italy might have had a second when Antonio Candreva shimmied with a neat stepover, only for his shot to be beaten away by Andreas Isaksson.
Sweden had a late penalty shout, though in truth this was a game Zlatan and co. never looked like winning, given their repeated failure to test Italy goalkeeper Gianluigi Buffon.
Italy's victory secures a place in the knockout stage and the Republic of Ireland awaits in Group E's final fixture, while Sweden takes on Belgium.