Bosnia, whose fate was sealed before their final Group F tie, got the goals through Edin Dzeko, Miralem Pjanic and Avdija Vrsajevic, while Reza Ghoochannejhad pulled one back for the Iranians at Arena Fonte Nova in Salvador.
Argentina ended top of the pool with a perfect nine points following a 3-2 win over Nigeria in a simultaneous fixture. The two countries advanced to the last-16 of the tournament.
Bosnia enjoyed a 1-0 lead at the break, as Manchester City striker Dzeko drilled a left-footed shot into the bottom corner from outside the box in the 23rd minute.
Carlos Queiroz's men nearly replied with interest a minute later, but Masoud Shojaei's deft chip beat Stoke City goalkeeper Asmir Begovic but not the crossbar.
The Europeans, who were making their debut at the Fifa spectacle, doubled their advantage in the 59th minute, as Pjanic clinically tucked away a one-on-one chance following a defensive lapse by Iran.
Goochannejad restored some slim hope for the Persian Stars when he tapped in from close range in the 81st minute.
However, Vrsajevic made it 3-1 moments later with an emphatic strike on the breakaway to seal the result for Safet Susic's charges.