Ante Vukusic fired Hajduk ahead in the 16th minute, drilling in a low shot after a one-two with strike partner Senijad Ibricic who converted a penalty in added time.
Sibenik squandered a hatful of good chances after the opening goal, striker Ermin Zec missing three sitters while Ivan Medvid and Jusuf Dajic also went close either side of halftime.
It was Hajduk's first trophy since 2005, when they last won the Croatian league title before traditional foes Dinamo Zagreb captured five in a row.
"It is very nice to be a part of Hajduk today and we are very proud to have played in this final and won the silverware," Hajduk coach Stanko Poklepovic said.
"We would have preferred to win the league and cup double but it is still a great feeling because it's my first trophy in a Hajduk shirt," added defender Josip Skoko.