Henny Reistad and Nora Mork led the way for the home team in attack, while Norwegian international Silje Solberg had a superb performance between the posts in just her second appearance in the Esbjerg goal.
Esbjerg was hit by an injury to Katharina Filter shortly before the last semi-final match and had to bring in Solberg as a late cover.
She did a fantastic job as the team progressed from the semi-finals, and on Wednesday, she also got off to a good start with a save on the very first shot from Odense.
From the start of the match, there was a fierce intensity in the match between the two best teams in the women's league.
Reistad looked sharp and put Esbjerg ahead 5-4 with three successive goals. Elin Hansson added three more, and with a goal each from Mork and Live Rushfeldt Deila, Team Esbjerg created a gap of four goals in the middle of the first half.
Mork was generally excellent both in her shot efficiency and in terms of creating assists for her teammates.
On the other hand, Odense's Elma Halilcevic kept the visitors in the game in the first 30 minutes with a string of important goals.
In the second half, Mork continued to control the game and after almost 35 minutes delivered another beautiful assist when she found Olivia Löfqvist with a pass behind her back, allowing Esbjerg to take a 23-19 lead.
Reistad followed up with three more goals, and the home team extended the lead to 26-21.
When Esbjerg took a 30-23 lead with just over 15 minutes left in the game, it started to look difficult for Odense.
With ten minutes left, Mork again showed her superiority with a look-away delivery for Rikke Iversen, who gave Esbjerg a ten-goal lead.
Esbjerg was simply too big a mouthful for the visitors, who must instead look ahead and focus on keeping their hopes alive in the return leg on Saturday.