The Norwich City man drilled home against the run of play on 82 minutes as Martin O'Neill's men seemed on course for a smash-and-grab victory in Zenica tonight.
However, Edin Dzeko pounced just three minutes later to throw the hosts a lifeline ahead of Monday's return leg in Dublin.
Here, Sports Mole analyses how the spoils were shared during a foggy encounter in Bosnia.
On target: 10
REPUBLIC OF IRELAND
On target: 3
Was the result fair?
Without a doubt. The Irish would have been stopped by Interpol in the airport had they come away with what would have been a robbery of sorts. The statistics do flatter the hosts somewhat, though, with very few of their 10 shots on target actually troubling goalkeeper Darren Randolph, who had one big save to make in the 90 minutes. They did not do enough to win, nor did the visitors, but Brady's goal has certainly tipped the tie in their favour ahead of the return leg on Monday night.
The question hanging over the hosts' night was whether they could continue to evolve under coach Mehmed Bazdarevic, who led them to five victories from a possible six in Euro 2016 qualifying this calendar year. That statistic looks more amazing now, and for the wrong reasons. Bosnia-Herzegovina were bitterly disappointing in both halves. Their heavy hitters never showed up. In Miralem Pjanic, they had a playmaker who had scored five and set up five in 10 Serie A games for Roma this season, though his end product was woeful tonight. Consequently, his club teammate Dzeko - who had netted eight times in qualifying - suffered terribly without a lack of service, as did his strike partner Vedad Ibisevic.
Overall tonight was a reminder as to why Bosnia - then under Safet Susic - had won just two points from their first four games in qualifying, following defeats by Cyprus and Israel. Bazdarevic's arrival changed things utterly, but there are still shades of complacency from this side and it may have just cost them a place in France next summer.
Republic of Ireland's performance
With Shane Long injured, and Jon Walters suspended, the goalscoring burden fell on Daryl Murphy's shoulders. The Ipswich Town striker had never scored for his country in 18 appearances, and this did not look like a duck-breaking night in a first half which saw him isolated. It was at the other end where the Boys in Green impressed, with Richard Keogh excellent alongside Ciaran Clark as the duo snuffed out chances time and again.
Despite a resolute defensive display, it was difficult to see where a goal would come for the visitors. In fact, seeing anything at all grew increasingly tough by virtue of a fog which hovered over the stadium for the entire second half. Visibility was limited, but the Irish still managed to sneak into a 1-0 lead when Brady galloped forward with Senad Lulic. A cute Ronaldo chop from the Irishman saw him work the ball on to his lethal left foot, as he drilled past Asmir Begovic with eight minutes of normal time to play, but Dzeko cancelled it out.
O'Neill would have certainly taken a 1-1 draw prior to kickoff, but given that victory was within touching distance, the Republic of Ireland boss can justifiably feel irked.
Sports Mole's man of the match
Richard Keogh: During the pre-match press conference, Keogh insisted that he was unfazed about coming up against the "high-calibre" Dzeko. On the back of this, the Derby County man was right not to be worried. Keogh was superb in both halves. In the first, he stuck to the Roma man like glue, whereas in the second period he pulled off a host of key interventions to thwart the big striker again.
It was a contest which threw up very individual errors, but Lulic could, and certainly should, have opened the scoring early in a fog-laden second half, but Randolph kept him out. Still, it was a moment which Bosnia-Herzegovina may well come to regret in this tie, with the Irish now favourites to progress into the finals by virtue of their away goal.
Felix Brych of Germany had a solid game. He brought a no-nonsense reputation with him to Bosnia, but he never once looked overly strict tonight in a contest which threw up just one yellow card - a first-half booking for Stephen Ward.
Both sides do it all again on Monday for the second leg in Dublin.