Odense, who won the regular season with maximum points last season, actually started well in Saturday's top showdown.
The visitors were ahead by two goals several times in the opening phase, but after Odense led 7-6, Esbjerg turned the tide.
Odense scored just three times in the last 18 minutes of the first half following a string of poor shots on goal, and Anna Kristensen's great play between the posts for the home team, who led 18-10 at halftime.
Odense managed to cut the deficit through a bright start to the second half, but technical errors and a sharp home team quickly took the sting out of the visitors again.
There was no excitement left in the last part of the second half, which was dominated by the home team, but the home team's fans could enjoy, among other things, ten goals by the Swedish winger Elin Hansson.