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The visitors made a bright start to the match, and took the lead on 13 minutes through Haris Medunjanin, who found the top-left corner of the goal from distance.
Cyprus grew into the match as the half went on, as Nestoras Mitidis and Georgios Efrem forced saves from Asmir Begovic, before Konstantinos Charalambidis found an equaliser on 32 minutes with an effort from close range.
The hosts took the lead less than 10 minutes later, as Constantinos Makridis found Mitidis in the box, who produced a clinical finish past Begovic.
Bosnia pegged Cyprus back immediately though, as Senad Lulic found Medunjanin with an inviting cross, before the midfielder finished from close range.
After the break, the visitors began to assert control on proceedings, as Pjanic hit a free kick over the bar, before Ibisevic dragged an effort narrowly wide of the right post.
The hosts almost found an equaliser before the final whistle, as Dossa Junior headed wide from close range, before Makridis dragged an effort narrowly wide in added time.