Serbia were one point adrift of Ireland ahead of this evening's game, while Wales were four points back in third place, but this evening's result restores Slavoljub Muslin's side to the top of Group D, with Ireland facing both sides in vital World Cup qualifiers later this year.
At Rajko Mitic Stadium in the Serbian capital, Welsh Aaron Ramsey scored from penalty in 35th minute, while Serbian Aleksandar Mitrovic equalized in 73rd minute.
Up next for the Republic is Georgia away on September 2, then they host Serbia three days later.
"(Bale) is who he is, he is one of the best players in the world but I firmly believe we have enough about us to get what we need here. We came to Serbia and got a result without him, that just shows the strength that we have. "He is a vital player for us and I look at Aaron even when Gareth is there", said Coleman.
"If we are serious about qualifying outright it's a game we can't lose", Coleman said.
The Wales global Aaron Ramsey may not have had the most stunning of seasons for Arsenal Football Club, but the reasons for that will surely be the subject of plenty of talk and right now are besides the point. They are four points behind the top two at the halfway stage, and defeat in Belgrade would seriously undermine their qualification hopes.
With two double-headers to come in September and October respectively, Ireland have two home and two away matches left to play.
Having praised Ramsey for an inspired display, Coleman was also delighted with his penalty, scored at the same end as Czech midfielder Antonin Panenka's original dinked spot kick against Germany goalkeeper Sepp Maier in the Euro 1976 final.
There was further concern in the Wales defence following some pinball in the visitors' box and Aleksandar Mitrovic, scorer of Serbia's late equaliser at Cardiff in November, sounded further warning of his aerial ability when he headed just wide.
But not only was Ramsey's spot-kick at the same ground once known as the Red Star Stadium, it was actually taken at the same end. "It was only a recce, but I had butterflies in my stomach", he said.
"Countless times I've been away on global duty as a player and a manager... little things which people probably wouldn't see", Coleman said. 'I think this team is fantastic.
"It's identical. It's what we thought as soon as he did it".
"But I had no doubt he'd score because he's playing with such confidence at the moment, his overall performance was absolutely outstanding".
The absence of suspended pack leader Gareth Bale and several other regulars should not stop Wales from firing.