Mladen Petric's vicious free kick had given Hamburg a half-time lead in the second leg at Craven Cottage, but Simon Davies and Zoltan Gera scored the two goals required to take Fulham though.
The Cottagers, who will be without suspended right-back Chris Baird for the second leg, must be admired for the way they held firm to the end, Schwarzer thwarting an angled effort from substitute MladenPetric on 88 minutes.