With a place at next year's finals in France at stake, it naturally turned out to be a tight game. However, Martin O'Neill's team performed superbly against a very good opponent.
There were few goalscoring opportunities in the first half for Ireland, but the hosts went close through Miralem Pjanic and Ervin Zukanovic but neither tested goalkeeper Darren Randolph.
By keeping their team shape, closing space down, and connecting their passes at key moments, Ireland were able to stifle their opponents and restrict their creativity in the final third.
When they did burst forward, there were flashes of excellence, as Brady showed with his net finish on 82 minutes when he cut inside his marker and fired in past Asmir Begovic.
Bosnia & Herzegovina got a goal back through striker Edin Dzeko, but Ireland held on for the draw, which gives them something to take confidence from ahead of the second leg in Dublin on Monday, November 16.
Ireland had several top performers, including defender Ciaran Clark, who admitted that the fog that drifted across the pitch in the second half made it a difficult game to get through.
"It was very foggy out there, especially in the second half. But it was the same for both teams. That's half the tie done and we've got to get ready for [the return on] Monday," said Clark afterwards.
Bosnia & Herzegovina: Begovic; Mujdza (Vranjes 51), Sunjic, Spahic, Zukanovic; Visca (Djuric 73), Pjanic, Cocalic, Lulic (Hajrovic 88); Ibisevic, Dzeko.
Republic of Ireland: Randolph; Coleman, Keogh, Clark, Ward (Wilson 67); Hendrick, Whelan, McCarthy, Brady (McGeady 86); Hoolahan (McClean 60); Murphy.
Referee: Felix Brych (Germany).