Henny Reistad and Michala Moller played strongly in the back chain, and goalkeeper Katharina Filter was hard on her German compatriots with 12 saves in the first half alone.
Dortmund were torn apart from the first minute by a well-prepared home team, keen on revenge for a miserable performance in Romania in the last round.
After just six minutes, Dortmund coach Henk Groener took his first timeout. By then, Team Esbjerg had scored on their first seven attacks and put themselves ahead 7-2.
For a while, the Germans managed to minimize the damage. Nine minutes before the break, Esbjerg's lead was still five goals, but then the home side upped the pace again.
After six successive Danish goals, Team Esbjerg opened a gap of 21-10, and at the break, the Danish vice-champions were ahead 24-14.
The match was effectively decided at half-time, so it was not surprising that Esbjergs' game lost a little intensity in periods of the second half.
After a bad spell for Team Esbjerg, the visitors managed to reduce the deficit to 26-32. But the visitors did not get any closer, and there was never any doubt whether Team Esbjerg would claim the two points.
Thanks to the win, Team Esbjerg now have six points after six games in the Champions League group stage.