The PSG frontman, who scored an incredible overhead kick against England in 2012, attempted to score a similarly impressive acrobatic goal but was foiled twice by the Iranian defence.
However, Ibrahimovic did find the net at the Friends Arena, heading home at the back post to give Sweden the lead on 11 minutes.
Sweden's No 10 scored and made another in a slick first-half performance, where the vast majority of the 33,773 crowd at the Friends Arena were cheering for the away team.
Sweden is home to more than 60,000 people who were born in Iran, and together with their children and grandchildren they packed the stands, outnumbering the Sweden fans and creating a cascading wall of noise for much of the match.
Ibrahimovic silenced them, albeit temporarily, when he gave Sweden the lead in the 11th minute.
His clever pass found Erkan Zengin, whose chipped return was powerfully headed home by the Sweden captain at the far post, despite the best efforts of Iran goalkeeper Alireza Haghighi to keep it out.
