Despite suffering a humiliating 6-1 defeat on Serbian soil in 2012, Coleman's charges started with some much-needed positivity when Chris Gunter almost got the better of Jagos Vukovic down the right flank, as the Dragons sought to set an early benchmark.
The stifling heat in Belgrade played a part in slowing proceedings throughout the first half, but the game was brought to life when Aaron Ramsey chased down a lost cause in order to earn a cheap free kick off Serbia keeper Vladimir Stojkovic, who had advanced recklessly out of his area.
The resulting free kick soon saw Luka Milivojevic penalised for an apparent shirt pull on Sam Vokes, leaving Ramsey with the chance to put his side in front from the spot. The opportunity was grasped confidently by the Welshman, who produced the most outlandish of Panenkas to send Stojkovic the wrong way.
The goal seemed to spur Serbia into action and they went close on two occasions before the interval, both Dusan Tadic and Nemanja Matic causing problems in the Wales box following some productive work on the wings.
The hosts came out of the traps quickest in the second period and they might have found a leveller through Aleksandar Kolarov, who sent his bending free kick just a few inches over the crossbar with Wayne Hennessey scrambling.
The run of play was very much with Serbia after the break, although Wales might have found an invaluable second goal early on, only to see Vokes send his thumping header from a corner over the crossbar from close range.
That miss was to prove costly for the visitors when substitute Aleksandar Prijovic produced an adroit back-heel to dumbfound a tiring Wales defence, leaving Aleksandar Mitrovic with the chance to fire cooly beyond a stranded Hennessey in the away goal.
The Dragons might have snatched an important late winner going into the final 10 minutes, but Serbia stopper Stojkovic had other ideas, as he kept out Ramsey's low effort following some standout creative play from an inspired Joe Allen.