Already eliminated after two losses, Bosnia, appearing at a major tournament for the first time as an independent nation, went ahead in the 23rd minute through Edin Dzeko, who drilled a left-foot shot past Iran goalkeeper Alireza Haghighi.
Bosnia doubled their lead just before the hour through Miralem Pjanic's cool finish in the box before Reza Ghoochannejhad pulled a goal back for Iran in the 82nd minute.
Avdija Vrsajevic restored Bosnia's two-goal cushion with a fine strike a minute later.
Iran had required all three points against Bosnia and needed Argentina to beat Nigeria to have any shot of grabbing a surprise place in the last 16. The Argentines beat Nigeria 3-2 in Porto Alegre to top the group.
(Writing by Peter Rutherford; Editing by Justin Palmer)
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