Although the Republic of Ireland had the better of their game at Stara Pazova, Serbia's Ivana Trbojevic hit the post with their only shot on target in the game.
Six minutes later and into the last quarter of an hour, Alannah McEvoy broke the deadlock with what proved to be the only goal of the match.
Scotland were in Belgrade for their clash with Hungary, which saw goals exchanged and the scoring completed in the first dozen minutes.
Katalin Tolnai scored for the Hungarians in the 8th minute and Morgan Cross got the quick equaliser.
The next Group 4 games are on Wednesday at 1pm (UK time), with Scotland again at Gradski for the meeting with Republic of Ireland.
The last round of games are then on Saturday, with only the group winners guaranteed progression to the finals.
Pictured - Action from Scotland v Hungary. (@MLSZhivatalos)