A goal in each half from Senijad Ibricic and Zlatan Muslimovic in Yerevan gave the points to the visitors, consolidating their position in second place in Group 5. There could have been more goals as Edin Dzeko missed a penalty for the the visitors in the first half and Artavazd Karamyan struck the woodwork for Armenia in the second.
Bosnia-Herzegovina are now clear favourites to qualify for the play-offs from the group, having taken 15 points from seven games, and could even challenge for first place should leaders Spain lose their perfect record. It took just five minutes for the visitors to take the lead.
Admir Vladavic set up Ibricic, who initially headed against the bar but was able to convert the rebound. As the visitors dominated, Armenia keeper Gevorg Kasparov made sharp saves to deny Wolfsburg striker Dzeko and Hoffenheim's Vedad Ibisevic.
And Bosnia-Herzegovina missed a glorious chance to go 2-0 up when they were awarded a penalty after 33 minutes, but Dzeko could not convert. Armenia's best chance of the half fell to Henrikh Mkhitaryan four minutes before the break, but his effort lacked conviction.
Bosnia took their foot off the pedal somewhat after the restart and almost paid the price when Karamyan's long-range effort was kept out by a combination of visiting keeper Nemanja Supic and post. With Bosnia-Herzegovina now limited largely to counter-attacks, the second goal was a relief when it arrived.
Dzeko made up for his penalty miss by supplying the cross for Muslimovic to convert 15 minutes from time.