The win puts Serbia four points clear at the top of the group with two games to play - away at Austria and home to Georgia - and relegated Ireland to third place, a point behind a resurgent Wales who they travel to in their final game.
Serbia, who like both Ireland and Wales went into the game with an unbeaten record, had the better early chances and deservedly took the lead on 55 minutes when Kolarov hammered a shot in off the bar to silence the home crowd.
They had to play the final quarter with 10 men after Nikola Maksimovic was sent off for a professional foul, and survived a justifiable penalty claim and a near miss from Daryl Murphy to leave Ireland's hopes of a playoff place hanging by a thread.
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(The story refiles to fix typo in Kolarov in headline, no change to story.)
(Reporting by Padraic Halpin; Editing by Alison Williams)
