Hamburg dominated from the off and inside the first 10 minutes Son Heung-Min had a shot saved.
In the 14th minute, however, they went ahead when Van der Vaart headed in a Marcell Jansen cross from inside the six-yard box.
Five minutes later it was 2-0 to the hosts and the Dutchman grabbed his second of the match with another close-range finish, this time with a shot.
Schahin could have had another on the hour mark but his well-struck effort from outside the box was kept out.
However, they were unable to grab an equaliser as Hamburg scraped through to take the points 2-1.