The victory was secured in the last two minutes, when Helena Elver proved her goal instinct in attack, while Amalie Milling made the crucial save at the opposite end.
The match was the first of two test matches this week between the two countries which will mark Jesper Jensen's last international matches in charge of Denmark.
The last stop on the national team coach's farewell tour is on Saturday in Aabenraa.
Despite the win there were plenty of Danish weak points against a well-prepared German team.
In the teams' last meeting in the European Championship intermediate round in December, Denmark clearly dominated proceedings, but the physically strong Germans proved a much more difficult task for the Danes on Wednesday.
Both goalkeepers, Katharina Filter and Anna Kristensen performed well at either end to keep the scoreline to a bare minimum as the home side led by 13-12 at the interval after a first half where both sides were guilty of wasting many chances.
After the break, the Danish women in particular improved their ability to convert chances into goals.
Both teams suffered from lapses in concentration as both teams struggled to create the decisive gap during the second half but the visitors still managed to claim all honors, when Elver and Milling both delivered at opposite ends to give Denmark yet another win against their southern neighbours.