Aleksandar Kolarov's thumping second-half drive in Dublin was enough to secure all three points for the visitors, who will now have their sights set firmly on Russia next year as they sit four points clear at the top of Group D with two games left.
Ireland's performance was a huge improvement on the underwhelming draw against Georgia on Saturday, but they were comfortably kept at bay by a dominant Serbian side, who played the last 20 minutes with 10 men after Nikola Maksimovic was sent off.
The loss is Ireland's first of the qualifying campaign and first in a competitive home game under Martin O'Neill and leaves them third trailing Wales in second by one point after their 2-0 win over Moldova.
Ireland host Moldova next month before travelling to Wales for what promises to be a mouth-watering occasion.
Maenwhile Turkey's Cenk Tosun scored a second-half goal to lead his nation to a 1-0 win over Croatia that blew Group I wide open in European qualifying.
The top four teams are now separated by just two points with two games left.
Group leader Croatia and Iceland have 16 points each, while Turkey and Ukraine are both just two points behind.
Tosun slammed the ball home in the 75th minute after Croatia goalkeeper Danijel Subasic was unable to hold on to a fierce drive by Oguzhan Ozyakyup at a packed stadium in Eskisehir.
The goal came as Croatia, led by playmaker Luka Modric, looked to be in control of the game.
In the other Group I matches, Iceland remains in the qualifying chase after a 2-0 win over Ukraine, while Finland beat Kosovo 1-0.