With their fate already sealed after defeats to Argentina and Nigeria, Bosnia played with freedom and made history as goals to Edin Dzeko, Miralem Pjanic and Avdija Vrsajevic saw them collect their first points at the showpiece.
The result also ended Iran's stay in Brazil, as they finished last in Group F with just one point from three matches.
Carlos Queiroz's side needed to beat Bosnia and hope Argentina defeated Nigeria, but saw their slim chances of progression end in Salvador on Wednesday.
The result means Nigeria – who were beaten 3-2 by Argentina – progress to the last 16 with Alejandro Sabella's side.
Bosnia – who had been on the front foot since kick-off – had their pressure rewarded in the 23rd minute when Dzeko, who proved an early threat, broke his World Cup duck.
The Manchester City forward won the ball 35 yards from goal and charged forward, evading two challenges before firing a low left-footed strike past Iran goalkeeper Alireza Haghighi, into the inside of the post, and in.
Iran were denied an immediate response when Masoud Shojaei's deflected effort from just inside the penalty area hit the crossbar after good work from Ashkan Dejagah on the right.
Ghoochannejad was the man responsible, applying the finishing touches to Javad Nekounam's dangerous low cross.
