The visitors, who began the day in fourth place in Group C one point behind Northern Ireland, were frustrated until the 66th minute when Marko Pantelic accepted a welcome gift.
Northern Ireland's Steve Davis failed to look when he steered a pass-back to Lee Camp and Pantelic stole in to round the stranded keeper and finish into an empty net.
"I hope we have restored some faith in Serbian soccer after this win," Pantelic told reporters.
"We are confident that the fans will get behind us in our remaining three matches and hopefully we will win a play-off berth to give them something to cheer about."
"Anxiety crept in after we failed to score in the first half but we desrved our win because we dominated the match.
"The group is wide open now and we have to stay focused to win our home match against the Faroe Islands on Tuesday."
