The home side made a bright start with Ruud van Nistelrooy threatening inside 60 seconds, with Cottagers keeper Mark Schwarzer snuffing out the danger.
Piotr Trochowski then fired a long-range shot narrowly wide as Hamburg made the early running.
Fourteen minutes in the visitors had their first chance, but Zoltan Gera's 25-yard effort following Bobby Zamora's flick-on was deflected wide and the resulting corner was cleared.
Hamburg then went back to dominating possession without being able to prise open a stubborn Cottagers backline who held firm for the remainder of a fairly low-key 45 minutes of football.
Early in the second half Zamora took a knock when trying a shot from well over 30 yards out and he soon had to be replaced, with Clint Dempsey taking over.
Fulham right-back Chris Baird was then cautioned, a booking which means he will miss the second leg at Craven Cottage next week - Trochowski would suffer the same fate later on in the game.
On the hour Gera found space down the inside left channel, but was unable to find Dempsey as he raced into the Hamburg area.
Gera then wriggled clear in the box after being found by Dempsey, but lost his footing as he prepared to shoot on goal.
Twenty minutes from time Schwarzer touched over a stinging drive from Jonathan Pitroipa and then he grabbed a David Jarolim effort at the second attempt.
As time ticked away the home side grew frustrated by their inability to break down the English side and the game ended in stalemate.