Cameroonian striker Aboubakar Oumaru headed Vojvodina's winner against OFK Belgrade in the 71st minute while Igor Stojakovic netted from close range shortly after halftime to put Javor in the driving seat against Jagodina.
The return legs are on April 17.
Vojvodina, bidding to reach their sixth cup final after losing the previous five, dominated from start to finish and missed a hatful of chances either side of Oumaru's far-post header.
OFK keeper Milan Lukac saved several fine saves and Vojvodina midfielder Enver Alivodic hit the woodwork as the visitors somehow held on to give themselves a fighting chance to advance.
"This was easily Vojvodina's best performance since I took over (last September) and we would have won by a bigger margin had it not been for a string of superb saves by Lukac," Vojvodina coach Nebojsa Vignjevic told Serbia's Arenasport television.
"OFK were worthy opponents and although we are in a good position we know that it will be a tough second leg."
Javor and Jagodina are both aiming for their first final and the hosts gained the upper hand after Stojakovic rounded of a flowing move when he took a through ball in his stride and scored from a tight angle.
Javor's Nigerian striker Ifeanyi Onyilo should have made it 2-0 in the closing stages, but skewed his shot from six metres wide of the near post after a darting run.
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- OFK Belgrade