Roy Hodgson's fairytale run started way back in July last year with a third-qualifying round tie against FK Vetra of Lithuania, and has since carried them through the group stages against Roma to superb performances which knocked out favourites Shakhtar Donetsk and then Italian giants Juventus - but could yet have its finest hour at the HSH Nordbank Arena.
Hodgson has also managed to keep Fulham on track in the Premier League, currently safe in 12th place - a remarkable achievement given the relative resources available to the west London club, so often in the shadow of their illustrious neighbours.
It was, though, no easy ride as a stunning 30-yard free-kick from Mladen Petric put the Germans in control.
However, Hodgson's side are resilient and fought back to level through a fine finish from Simon Davies, before Zoltan Gera fired in a winner with 17 minutes left to send Fulham to an unlikely, but hugely deserved first European final.
Striker Bobby Zamora - who had been given a pain-killing injection in his troublesome Achilles to be fit to start - had a half-chance during the opening minutes after a one-two with Gera.
However, Hamburg keeper Frank Rost stood up well, before Fulham's 19-goal striker scuffed the rebound wide.
Brede Hangeland headed over as the home side continued to press.
Hamburg, though, looked dangerous on the break, lead by former Manchester United striker Ruud van Nistelrooy, as the Germans played with more freedom than in the first leg - now under the guidance of former Tottenham skills coach Ricardo Moniz after Bruno Labbadia was sacked.
John Pantsil and then Aaron Hughes both made a timely block as the visitors looked to swing more dangerous balls into the Fulham box.
There was, though, little anyone could do to prevent Hamburg taking the lead on 22 minutes.
Danny Murphy fouled Jose Ze Roberto 30 yards out, and Petric - whose goal at Wembley in the final match of the Euro 2008 qualifying campaign ended Steve McClaren's reign as England boss - stepped up to crash a glorious left-foot curling free-kick past Mark Schwarzer and into the top corner to give the Germans a crucial away goal.
The majority of Craven Cottage - which has played host to some memorable European nights this season, including a famous victory over Italian giants Juventus - was left in stunned silence but for the delirious visiting supporters, now dreaming of a place in next month's final at their HSH Nordbank Arena home.
On 32 minutes, Fulham had a chance to respond when Guy Demel tripped Simon Davies, but the Welshman crashed his 25-yard free-kick high over the crossbar.
Just before the interval, Jonathan Pitroipa latched onto a long ball and rounded Schwarzer, but the effort was correctly ruled out for offside.
Hodgson admitted it had been something of a gamble to play Zamora, and less than 10 minutes into the second half, the striker was replaced by American Clint Dempsey.
The home fans were screaming for a red card when Jerome Boateng - younger brother of Portsmouth's Kevin-Prince - jumped into a challenge on Gera, with studs showing, but winning the ball and Turkish referee Cuneyt Cakir brandished only a yellow.
From the resulting free-kick, Paul Konchesky played a clever ball into Damien Duff, but his shot rolled just inches wide of the far post.
Schwarzer stood up well to an angled drive from Hamburg captain David Jarolim.
Fulham were level on 69 minutes.
Murphy's perfectly-weighted chip to the edge of the penalty area picked out Davies, who brilliantly turned Demel before knocking the ball past Rost as the Cottage erupted.
Pitroipa broke clear down the left, but drilled wide.
With the Germans still leading on away goals, Fulham had to go for it, so Hodgson sent on Erik Nevland, replacing full-back Pantsil.
The Cottage was rocking again moments later, as Fulham went ahead on 76 minutes.
A corner was only half-cleared, and Gera was first to react as the Hungarian swivelled to lash the loose ball into the net.
There were some three minutes of stoppage time, during which van Nistelrooy dragged an angled shot wide.
When it came, the final whistle was greeted by cheers loud enough to be heard at Stamford Bridge - as Hodgson and his team celebrated the most unexpected, but richly deserved, of achievements.