The club are under threat of surrendering their record as the only German top-flight ever-presents after producing a toothless home display on Thursday.
Mirko Slomka's side, who finished 16th in the Bundesliga, did have chances to break the deadlock, with Pierre-Michel Lasogga and Hakan Calhanoglu spurning the best of them.
A score draw on Sunday will see them preserve their safety on the away goals rule, and the first-leg draw at least ended a run of five consecutive losses at the end of their league campaign, with Hamburg only rescued from automatic relegation by the similarly miserable form of Eintracht Braunschweig and Nuremburg.
Their opponents Greuther, on the other hand, come into the second leg having lost just once in their past 16 matches, and only missed out on automatic promotion by two points after finishing third behind Paderborn.
In Ilir Azemi, they boast the second tier's third highest scorer with 14 goals, and Hamburg will have to be wary of a side that scored more than any other in the regular Bundesliga 2 season.
Greuther also hold a strong home record, having lost just once in their past 10 league matches at the Trolli Arena.
By contrast Hamburg have been abysmal on their travels this season, with their last victory on the road coming on October 27, a 3-0 win at Freiburg.
Following Thursday's stalemate, Hamburg playmaker Rafael van der Vaart conceded that their performance at the weekend had to be vastly improved.
"Furth played very well," he said. "We were better in the second half, but we have to do much better on Sunday."
