Their astonishing 5-4 aggregate success was all the more remarkable as former European champions Juve, 3-1 ahead from the first leg of the last 16 tie, had extended their advantage in the second minute through David Trezeguet.
But the competition favourites imploded after Italy's World Cup-winning captain Fabio Cannavaro was sent off in the 28th minute for bringing down Zoltan Gera.
VIDEO:Dempsey's dink
A night that started so well for the Italians turned into a nightmare as they finished with nine men after Jonathan Zebina was sent off just before the end for kicking out at Fulham's inspirational Ireland midfielder Damien Duff.
Asked if it was the Premier League club's greatest night Fulham boss Roy Hodgson told reporters: "It must come close because we had a terrible start conceding a goal after only two minutes.
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"But the crowd got behind the team and by half time I thought it was possible to turn it around and that's what happened.
"We were without senior players like (captain) Danny Murphy and Andy Johnson but we still won it. That's an incredible achievement for this club against the likes of Juve."
The victory was sweet for former Inter Milan manager Hodgson whose old team knocked Fulham's west London rivals Chelsea out of the Champions League in the last 16 on Tuesday.
By the time Cannavaro was sent off, Fulham had cancelled out Trezeguet's early strike with a superbly taken equaliser from Bobby Zamora after nine minutes.
They went into the break 2-1 ahead when Gera scored in the 39th minute after Fulham hit the bar and post through Simon Davies and Dickson Etuhu in a two-minute period before the goal.
EARLY PLAY
Juventus, with Diego, Trezeguet and Mauro Camoranesi dictating the early passages of play, seemed to lose their shape, ideas and conviction after Cannavaro was dismissed.
Fulham, meanwhile, grew in stature and confidence, boosted by the frenzied support of a 23,000 crowd who added to the memorable atmosphere at a packed Craven Cottage.
The home side responded with inspired play all over the pitch and fully deserved to go 3-1 ahead on the night and make it 4-4 on aggregate after 49 minutes with a penalty.
Dutch referee Bjorn Kuipers harshly awarded the spot kick after a cross from Duff hit Diego on the hand.
Gera gave veteran goalkeeper Antonio Chimenti no chance with the penalty for his second goal of the night as Juventus increasingly looked like a reeling punch drunk boxer.
Fulham continued to press for the winner to avoid extra time and when the
