Hamburg did almost all of the attacking but were denied by visiting goalkeeper Mark Schwarzer who was in inspired form, denying Jonathan Pitroipa, Piotr Trochowski and David Jarolim in quick succession midway through the second half.
Fulham, playing the 17th match of a Europa campaign which began in Lithuania in July, were forced to make the 1,000-km journey by road because of the widespread disruption to flights across Europe.
The trip included a three-hour delay in traffic on a German motorway.
Hamburg, who will host the final on May 12, began the tie without striker Mladen Petric who was recovering from a groin injury.
"It was not such a bad result, if we score once in the return (next Thursday) they must score two and I think they will have to come out and attack more than they did today," said the Croatian who came on as a second-half substitute.
EARLY CHANCE
Ruud van Nistelrooy had an early chance for the Germans when he burst into the penalty area but Schwarzer began an impressive performance by smothering the ball.
Trochowski went close with a 25-metre effort before Zoltan Gera had Fulham's best effort, a 20-metre shot which took a deflection.
Hamburg had their best spell in the second half when Pitroipa produced a snap-shot from a narrow angle which Schwarzer pushed over.
The Australian did well again to get his fingertips to Trochowski's dipping 30-metre drive and stop a Jarolim effort which went through a crowd of players.
Joris Mathijsen then foiled a Fulham counter-attack when he cut out Gera's pass to Clint Dempsey.
Petric added some bite to Hamburg's attack, forcing Schwarzer to make another difficult save before narrowly missing the target with a long-range effort.
