The result left the Bosnians in a good position to clinch at least a play-off berth in Group D, having collected seven points from four matches after Dzeko headed home an 83rd-minute winner in front of a capacity 15,000 crowd on a bumpy pitch.
Their quest, however, could be derailed by a squabble in the Bosnian Football Federation (NFSBiH), which has been given an April 1 deadline by UEFA to replace its three-man rotating presidential system with one in line with FIFA and UEFA standards.
A Congress the NFSBiH has scheduled for Tuesday is the body's last chance to adhere to UEFA's instructions and avoid suspension from international competition for the Balkan country's national team and clubs.
Adrian Mutu missed a sitter to double Romania's lead shortly after the break and they were punished several minutes later when Vedad Ibisevic glanced a teasing Zvjezdan Misimovic cross into the far corner.
