Safet Susic’s team finished level on 25 points with Greece at the summit of Group G, but their superior goal difference gave them top spot and an automatic place in Brazil next summer, their first ever berth in a major international tournament.
Vedad Ibisevic struck the all-important goal with just over 20 minutes to go, rendering Greece’s concurrent 2-0 triumph against Liechtenstein a result of no consequence.
Bosnia have suffered a series of near misses during recent years in their bid to qualify for an international competition, most notably losing to Portugal in the playoffs for both Euro 2012 and the 2010 World Cup.
Russia also narrowly beat Portugal by one point to first place in Group F, wrapping up their spot in Brazil despite a 1-1 draw at Azerbaijan.
Roman Shirokov’s first half goal was cancelled out by Javadov’s injury-time equaliser, but Azerbaijan had no time left to push for a winner, meaning that Portugal’s 3-0 win over Luxembourg was not enough for Paolo Bento’s men to escape the playoffs for the third international tournament in a row.