Although the German hosts dominated possession in Thursday night's first leg at the Nordbank Arena, they never really looked like breaking through until a late flurry.
The two sides will reconvene in a week's time at Craven Cottage with Roy Hodgson's men hopeful of getting the win that would seal a first European final.
There is still work to do of course, and Ruud van Nistelrooy must be kept quiet by a defence that will lack the suspended Chris Baird, but there was enough evidence to suggest Fulham's 18th match in a European campaign that began in Lithuania nine months ago will not be their last.
Hamburg were a force three decades ago, when they were powerful enough to lure Kevin Keegan away from Liverpool and then win the European Cup in 1983.
Those days are long gone. Hamburg can still attract big-name forwards, but even van Nistelrooy would accept his best days are behind him.
Not that the former Manchester United star has lost his eye for goal, it is just that the pace he did have has been reduced still further.
Time was when he would have held Aaron Hughes off and snaffled the opportunity that came his way after barely a minute.
This time the Fulham defender was quick enough to react and nudge van Nistelrooy aside, allowing Mark Schwarzer to quell the danger.
It was the start of a one-sided opening period in terms of possession.
Yet, as Barcelona found out 48 hours earlier, possession does not mean much if it cannot be turned into goals.
Hamburg's attacks got less frequent as the half wore on.
Paolo Guerrero failed to take the best chance that came his way, and when Jonathan Pitroipa got to the byline, instead of cutting the ball back to an expectant team-mate, he rolled it straight through to Schwarzer.
That the Fulham goalkeeper was underemployed was largely due to the efforts of a watertight defence, marshalled superbly by Hughes and Brede Hangeland, and the screening midfield talents of Danny Murphy.
It might not have been the greatest spectacle but the hardy 1,000 or so Fulham fans who had made it to northern Germany for one of the most fabulous nights in their club's history were not fussed about that as Hamburg continued in vain to look for an opener.
After giving the impression of not quite being fit all evening, Fulham's 19-goal talisman Bobby Zamora eventually ambled off seven minutes after the restart without so much as having a shot with which to mark the occasion.
Zamora's exit raised inevitable question marks about the journey, which Hamburg will not have to undergo themselves.
Still, after shrugging aside Shakhtar Donetsk, Juventus and German champions Wolfsburg in the knockout section of the competition alone, Fulham are unlikely to let that spoil the party.
And if David Jarolim had not stretched out to intercept a Zoltan Gera cross bound for Zamora's replacement Clint Dempsey on the hour, the Cottagers would have been in dreamland.
Hamburg responded with their most productive spell of the game.
Pitroipa, Piotr Trochowski and Jarolim all scorched Schwarzer's fingers to various degrees as Fulham finally showed signs of collective weariness before Mladen Petric nearly found the target at the end.
The tie remained goalless though, which will make Craven Cottage one pretty fine place to be for the return.