Now, the two sides will meet again in Dublin on Monday night to determine which of them will secure their place at next summer's European Championships in France.
When the Irish squad boarded the plane for Bosnia, head coach Martin O'Neill would probably have taken a score draw had you offered it to him.
After all, he was without some key squad members because of injury and suspension, while he had also been quick to highlight the quality of players that were at the disposal of his opposite number Mehmed Bazdarevic.
However, the fact that Ireland took an 82nd-minute lead, only to see that cancelled out by Dzeko just three minutes later, is likely to have resulted in some lingering disappointment.
On a more positive note, O'Neill's men are unbeaten from their last eight home encounters at the Aviva Stadium. Furthermore, in terms of competitive fixtures, the Greens have not tasted defeat in front of their own supporters since Sweden headed back to Scandinavia with a 2-1 win in September 2013.
They also have recent positive memories of the playoffs, having qualified for Euro 2012 via that route with a win over Estonia four years ago.
Were Ireland to progress on this occasion, it will secure their third involvement at the Championships.
Recent form: DWWWLD
The Bosnians dominated much of the first leg, both in terms of shots at goal and the possession.
Bazdarevic's charges had 63% of the ball over the course of the 90 minutes and created 11 chances to Ireland's four, yet they would have lost the encounter but for Dzeko's intervention five minutes from the end.
That goal from the former Manchester City and current Roma frontman has given his nation hope that they will now be able to qualify for the European Championships for the first time, although Bazdarevic has admitted that his team must improve.
"All is not lost. We didn't put on the kind of performance we aimed to and Dzeko's goal hauled us back into it," he told reporters.
"That gives us a better chance for rematch. We have the strength and quality, but we have to show much more of it to get a ticket to France."
They will make the trip to the Irish capital in good form, having lost just one of their last eight matches, five of which they have won.
Recent form: WLWWWD
As for Shane Long, he has recently returned to training following a month-long layoff with a knee injury, so he could be in contention for a place among the substitutes.
Meanwhile, Everton midfielder Muhamed Besic is expected to be included for Bosnia, having been banned for the home leg.
ROI possible starting lineup:
Randolph; Coleman, Keogh, O'Shea, Ward; Hendrick, Whelan, McCarthy, Brady; Hoolahan; Walters
Bosnia possible starting lineup:
Begovic; Mujdza, Sunjic, Spahic, Zukanovic; Visca, Pjanic, Besic, Lulic; Ibisevic, Dzeko
Head To Head
Prior to the draw on Friday, the only other clash between these two came in a friendly three years ago when Long's goal in the 78th minute was enough for hosting Ireland to claim a 1-0 victory.
We say: ROI 1-1 Bosnia
With the enormity of the prize that is at stake, this is likely to be a tight and nervy affair in Dublin. With that in mind, it would not be a surprise if the encounter were to go through extra-time and all the way to penalties.