Hamburg have never been demoted from the Bundesliga since its formation in 1963, but have struggled this season and only avoided automatic relegation by one point.
They face Greuther, who finished third in the second tier, over two legs for a place in the top flight next term.
Netherlands international Van der Vaart believes Hamburg must gain an advantage from the first leg at the Imtech Arena.
"We have to make our own game," he told Bild. "Then we have a good chance.
"How we play at home will be crucial. It is important in Hamburg to get a good result.
"They will come with confidence.
"As third in the table in the second league, they have played a good season. It will be a very close duel."
The two sides met earlier in the season in the DFB-Pokal, with Hamburg winning 1-0.
Hamburg also avoided defeat when the two sides met in the Bundesliga during the 2012-13 season prior to Furth's relegation.
