Miralem Pjanic was the real star of the show, but it was Vedad Ibisevic and Miroslav Stevanovic who got their names on the scoresheet for Safet Susic's side. The Stuttgart forward struck early on in the first half from close range, before Stevanovic rubbed salt in the wounds to secure the visitors' first win in six games.
Gareth Bale aside, Wales offered very little in Llanelli. A host of defensive mistakes led to their downfall and Coleman will know that a lot of hard work is required before they begin their World Cup qualifying campaign against Belgium in September.
The game came alive within the first minute when the home side almost gifted the visitors the lead. A hesitant Ashley Williams failed to deal with a routine long ball, which allowed Edin Dzeko to nip in and take advantage of his nervy defending, only to see his narrow drive well saved by Boaz Myhill.
Moments later Wales came within inches of opening the scoring on two separate occasions in quick succession. Gareth Bale took on two men on the right wing before slipping in new Liverpool signing Joe Allen behind the Bosnian defence. Allen cleverly squared for the oncoming Sam Vokes, who was only denied a simple tap-in by a desperate last-ditch clearance.
From the following corner, the hosts came even closer. Stoke keeper Asmir Begovic was called into action to produce a fingertip stop from Allen's arrowed volley, tipping the ball onto the bar.
Shortly afterward, it was Bosnia's turn to hit the woodwork as the flurry of goalmouth action continued. Defender Boris Pandza smashed a header against the crossbar from close range, getting on the end of an inviting corner from the left, leaving Myhill rooted to his spot.
Both sides showed composure in the ball, but the Bosnians always looked the more likely to open the scoring. And that moment came on the 20-minute mark, when Neil Taylor was caught dawdling on the ball by Mirsolav Stevanovic, who squared smartly for the onrushing Ibisevic to fire past the hapless Myhill.
In truth, the goal was deserved as Wales struggled to counter Bosnia's smart interplay and movement in midfield, and Manchester City's Dzeko was picking the ball up in dangerous positions far too easily.
However it was another Welsh mistake that should have seen Bosnia double their lead. Aaron Ramsey was caught in possession midway in his own half and Stevanovic played in Ibisievic, who turned Williams, opening up space ahead of him as he broke through on goal, only to drag his shot disappointingly wide.
Wales improved towards the end of the half, and it was the dangerman, Bale, who posed the greatest threat. The Tottenham winger took down a trademark diagonal cross-field ball from Ashley Williams and looked to lob Begovic in the Bosnia goal, but the shot never really had much chance of beating the Stoke man.
A few moments later, Bale also powered in a downward header from a floated Neil Taylor cross, only for Begovic to collect without too much trouble at the second attempt.
It was more of the same at the start of the second half with Miralem Pjanic continuing to pull the strings in midfield, producing pass after pass and unlocking the Welsh defence with his pinpoint through-balls.
Bosnia's second came after a catalogue of errors from the Welsh. The away side broke forward and worked the ball to the right hand side, where Stevanovic broke in to the box and then produced a sweet strike to fire into the top corner from a tight angle.
Craig Bellamy provided a lift for Wales after coming on midway through the second half, looking lively down the left wing and delivering a number of promising balls into the box.
A clearly tiring Bosnian side laboured to the final whistle knowing the win was all but confirmed, but their defence remained sturdy as Wales pressed for an unlikely comeback. Dzeko had a handful of opportunities to extend his side's lead towards the end of the game, but his wasteful finishing kept the scoreline at 2-0 to the visitors.