Two late goals handed Wales Under-21s a fifth straight win in their European Championship qualifying campaign.
Boubacar Dialida Diabang put the home side ahead just before the hour beating keeper Owain Fon Williams with a 20-yard shot.
Substitute Simon Church looked to have saved a point in the 86th minute.
But a minute later, Ched Evans grabbed the winner leaving Wales needing just one win from the last two games to finish top of their group.
"It was looking as if it wasn't going to happen, we needed a spark and Simon gave us that.
"We didn't play well, we can perform better than that, but the message was go and win away from home.
"Now it is all down to us for the next game."
"It was a great end. I didn't think we were going to come back after they scored because they were putting 10 men behind the ball every time.
"The pitch was terrible, they were physical and were doing everything to wind us up, but we stayed strong.
"It's a great feeling (to score) and it shows a sign of a good team who win and not play well."
Bosnia-Herzegovina U21: Buric, Colic, Benovic, Cejvanovic, Covic, Likic, Jelic, Aganovic, Zec, Dialiba, Zivkovic.
Subs Not Used: Sehic, Handzic, Puric, Masic, Papaz, Huseinovic, Stokic.
Goals: Dialiba 58.
Wales U21: fon Williams, Gunter, Rhys Williams, Mike Williams, Jacobson, Allen (Brown 77), Ramsey, MacDonald, Collison, Evans, Vokes.
Subs Not Used: Taylor, Basey, Bradley, Edwards, Wilson.
Booked: Vokes.
Goals: Church 86, Evans 88.
Ref: Alexey Kulbakov (Belarus).
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