Aleksandar Mitrovic again denied Wales victory as Chris Coleman's men were held to a fifth consecutive draw in World Cup qualifying after their match in Serbia on Sunday ended 1-1.
Wales have not reached a World Cup since 1958 and they remain four points behind their opponents at the Group D summit after goals from Aaron Ramsey and Mitrovic.
Although Wales' winless run goes on without suspended star man Gareth Bale, they will surely ruefully reflect on the opportunities passed up in four consecutive draws prior to visiting Belgrade - rather than a hard-fought point here - if they fail to close the gap to Serbia.
The unwanted streak includes a draw secured by Mitrovic's late header for Serbia in Cardiff in November.
The hosts' unbeaten record against Wales was threatened again by Arsenal star Ramsey's nonchalant first-half penalty.
But, once more, Mitrovic proved their nemesis with a clinical left-footed strike - a fifth of the campaign - to move his side back above Republic of Ireland, who also have 12 points, on goal difference at the top of the table.
After 25 minutes - and a very slow start - Serbia started to build momentum and a series of teasing crosses into the box saw Mitrovic nod wide of the left-hand post and then over the top.
But two rash defensive decisions from the home side at the other end handed Wales a 35th-minute lead they scarcely deserved.
Goalkeeper Vladimir Stojkovic foolishly attempted to shield a long ball out of play on the right and dragged Ramsey to ground, conceding a free-kick from which Luka Milivojevic's tug on Sam Vokes' shirt saw a penalty awarded to the visitors.
Ramsey stepped up to brilliantly chip his spot-kick into the corner, echoing Antonin Panenka's famous penalty at the same end of this stadium in Euro 1976.
As Wales looked to sit on their lead heading into the second half, Joe Allen's booking resulted in another potentially crucial suspension and Aleksandar Kolarov sent the subsequent free-kick fizzing just past the top-right corner.
Vokes headed just over in a rare Welsh attack, but the visitors' brave defence was finally breached with only 17 minutes remaining.
Aleksandar Prijovic ran in behind to meet fellow substitute Nemanja Gudelj's pass and nudged a flick into Mitrovic's path, the Newcastle United forward controlling well and finishing superbly beyond Wayne Hennessey.
Both sides then went hunting a winner, with Ramsey drawing a smart save from Stojkovic and Mitrovic acrobatically volleying wide.
Serbia ended the game on top, but their in-form forward flicked wide when granted another clear sight of goal and Slavoljub Muslin's men had to settle for a point that nonetheless ensured they returned to first place.