Zinnbauer – the club's former under-23 coach – replaced Mirko Slomka in the top job at Hamburg last month.
And while Zinnbauer's arrival coincided with a goalless draw against two-time defending Bundesliga champions Bayern Munich, a loss at the second-placed Borussia Monchengladbach was followed by a heartbreaking 2-1 defeat against Eintracht Frankfurt last week.
Hamburg – who beat second-tier Greuther Furth on away goals in last term's relegation play-off – dominated for much of their home clash against Frankfurt, only to lose to Lucas Piazon's stunning stoppage-time free-kick.
And a trip to Dortmund, who have finished in the top two for the last four years, means Zinnbauer's men will have to be at their best to claim their first win of the season.
"Joe is doing a very good job and is very emotionally involved," Biersdorfer told Hamburg's official website.
"You can see that something is stirring. He sends a team out after talking a lot of sense to them.
"The situation is difficult... we are in bottom place. Now everyone at the club and inside that dressing room must invest even more effort."
Hamburg will take heart from Dortmund's patchy recent form, which has seen them fail to win any of their last three league matches.
A 2-1 defeat to arch-rivals Schalke last week saw them drop to 12th – a position that is unlikely to last for long.
Hannover's bright start to the season has faded somewhat, with two losses in their last three, and they head to Munich to face a Bayern side who have hammered them in recent times.
