The return leg will be played in Zagreb on May 22.
Hajduk, who also won nine cup titles in the former Yugoslavia, fell behind early in the second half when their captain Mario Maloca gave the ball away in the penalty box and presented midfielder Domagoj Antolic with a simple finish.
The home side turned the match on its ahead in only three minutes midway through the second period, with Ivorian winger Jean Evrard Kouassi at the heart of their fightback.
The teenager first set up substitute Anton Maglica to draw level with a crisp finish barely a minute after coming on and then rifled in the winner after he was put through by Antonio Jakolis.
Maglica nearly added the third for Hajduk in the closing stages, when his powerful header cannoned off the woodwork.