Zinnbauer was promoted from his role as Hamburg's Under-23 coach on Tuesday, after Mirko Slomka became their fifth managerial casualty in just over three years.
The little-known 44-year-old has been charged with the sizeable task of preserving the club's unique record of having appeared in every Bundesliga campaign.
Hamburg have picked up just one point from a possible nine – and failed to score – so far this season, and Zinnbauer knows that things are unlikely to get any easier against the champions.
"No team dominates football matches like Bayern," said the new coach ahead of Saturday's encounter. "It's important we play as a unit.
"The problems have been the players' mentality. Results depend on the quality of the team, not the quality of individuals.
"I can promise that my players will be fired up. We will play with pure emotion."
Zinnbauer will aim to get the best out of captain Rafael van der Vaart and fellow playmaker Lewis Holtby, while Bayern coach Pep Guardiola could hand a start to Arjen Robben after he returned from injury as a substitute in their 1-0 UEFA Champions League win over Manchester City on Wednesday.
Fourth-placed Borussia Dortmund will look to build on an impressive 2-0 win over Arsenal in Europe in midweek at Mainz on Saturday, where Japan team-mates and close friends Shinji Okazaki and Shinji Kagawa will be under the spotlight .
The former is the Bundesliga's joint top scorer with three, while the latter made a superb start to his second spell at Signal Iduna Park against Freiburg last weekend.
Sunday's matches feature early leaders Bayer Leverkusen - seeking to respond to a narrow Champions League loss at Monaco when they take on Wolfsburg - and fifth-placed Borussia Monchengladbach, who clash with rivals Cologne.
Monchengladbach will look to in-form Andre Hahn to inspire them to victory over Cologne, who have kept clean sheets in four successive matches in all competitions.
Schalke and Stuttgart, on one point apiece, target their first victories of the season at home to Eintracht Frankfurt and Hoffenheim respectively.
And another two teams on one point, Hertha and Freiburg, kick off the fixture round in Friday's game, while Augsburg and Werder Bremen meet in Bavaria 24 hours later and Paderborn host Hannover.
