Klaassen scored the first from a penalty just before half time and the second from a pass by Justin Kluivert at the beginning of the second half.
The 2-0 home win means Ajax are in a good position to qualify for the semi-finals of the competition, which they have not reached since 1997. The return match takes place at the Veltins stadium in Germany next Thursday.
Ajax will also meet Heerenveen in the Dutch Eredivisie competition this weekend. Ajax are just one point behind leaders Feyenoord with four matches to go.