The victory saw Serbia leapfrog the Irish as they moved up two places to third spot, level on seven points with a Slovenia side that lost 1-0 at home to group leaders Italy who have doubled their advantage to six points.
It was also the first competitive win for Serbia coach Vladimir Petrovic, who started his reign in October with a shock 3-1 home defeat by Estonia before he racked up wins in friendlies against Bulgaria and Israel.
The Serbs, playing without the support of their fans who were banned from attending the match after causing a riot during last October's qualifier in Italy, fell behind to a 40th-minute header by defender Gareth McAuley from a deep Chris Brunt cross.
The Irish, roared on by 250 of their supporters who were allowed to watch from the stadium's VIP box, applied the early pressure but Serbia missed two good chances through Adem Ljajic and Branislav Ivanovic in an uneventful first half.
"We were below par in the opening period and the must-win pressure obviously got to the players, but we raised our game after the interval and deserved the three points," a relieved Petrovic told reporters.
"We let in a very soft goal and we must make sure that doesn't happen again in the upcoming matches," he said.
As the hosts appeared to have settled into the unfamiliar atmosphere of hearing their own voices echoing around the 55,000-seater, McAuley ghosted in at the edge of the six-yard box to head in Brunt's freekick from just inside Serbia's half.
Serbia's half-time substitutions, which saw Milan Jovanovic and Milos Ninkovic come on for Ljajic and the ineffective Nenad Milijas, paid dividends for the home side.
"We will have Vidic back for Estonia and we are also hopeful that Nikola Zigic might recover for what is another vital game in our bid to reach the finals," Petrovic said.
"We had an outstanding first half and got the all important goal but you have to give credit to Serbia for coming back into the match the way they did," he said.
"We knew that they have some very good players, that's football and we just have to live with it."
