The result left the Bosnians on a maximum nine points from three games, ahead of Austria who have three points from two matches. Northern Ireland have none from three games.
Both sides missed chances in an end-to-end contest, with Dzeko firing the home side ahead in the 27th minute when he steered the ball into the bottom left corner from 10 metres after a defensive blunder by Jamal Lewis.
Midfielder George Saville twice came close for Northern Ireland while Dzeko fired over the bar and had a superb goal controversially disallowed for offside at the other end in a see-saw first half.
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Substitute Gavin Whyte missed a gilt-edged chance to equalise in the 56th minute before Dzeko struck again in the 73rd, side-footing the ball past goalkeeper Bailey Peacock-Farrell after a defence-splitting pass by Miralem Pjanic.
Bosnia keeper Ibrahim Sehic kept out Saville's piledriver before Northern Ireland hit the woodwork for the third time in the dying minutes, as the home team's defender Ervin Zukanovic deflected a low cross from the right.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Pritha Sarkar)
