Although Wales were enjoying the better of the play it took three second-half goals to make all three points safe.
Bournemouth midfielder Sam Vokes gave Wales a cushion with an assured strike on 54 minutes, with Ched Evans and Jack Collison adding gloss to the scoreline.
Wales now trail Group 10 top pair Romania and France by five points but have two games in hand, with the next against the French at Cardiff's Ninian Park on Tuesday night.
Wales U21: Fon Williams, Blake, Jacobson, Ramsey, Mike Williams, Rhys Williams, Allen, Vokes, Evans, MacDonald, Collison. Subs: Adams, Church, Neil Taylor, James, Ribeiro, Bradley, Rhys Taylor.
Goals: MacDonald 29, Vokes 54, Evans 72, Collison 86.
Bosnia-Herzegovina U21: Pandza, Benovic, Ristanic, Covic, Papaz, Vrsajevic, Kasapovic, Zec, Jelic, Stilic, Buric. Subs: Likic, Peric, Zadro, Cejvanovic, Huseinovic, Salcinovic.
Ref: Stefano Podeschi (San Marino).
BBC