Clint Dempsey's wondergoal finally booked the Cottagers' place in the quarter-finals, but his 82nd minute strike was merely the icing on the cake of a famous night in the long history of the west London club.
The odds were firmly stacked against Fulham progressing as they trailed 3-1 from the first leg in Italy last week.
Things got ever worse for the Cottagers when they fell even further behind to a David Trezeguet goal with just two minutes on the clock.
The France striker was given a second bite of the cherry to bury Hasan Salihamidzic's low cross with a precise finish from 12 yards.
However, the Fulham fightback began just seven minutes later when Bobby Zamora chested down Paul Konchesky's cross and shrugged off the attention of Fabio Cannavaro before bagging his 16th goal of the season.
The tide began to turn on the half-hour mark when Cannavaro was sent off for hauling down Zoltan Gera as the last man.
Veteran keeper Antonio Chimenti pulled off a superb one-handed save from Zamora's curling free-kick before the Cottagers rattled the woodwork on two separate occasions as they began to sense an unlikely upset.
The home side edged their noses in front on the night when Gera lofted Simon Davies' cut-back into the roof of the net from close range on 39 minutes.
It was advantage Fulham at the interval as the Juve players trudged off down the tunnel and 25,000 fans packed inside Craven Cottage really started to believe in the impossible when they levelled the tie on aggregate on 49 minutes.
Diego was adjudged to have handled Damien Duff's cross in his own box and Gera held his nerve to rifle his spot-kick past Chimenti to make it 4-4 on aggregate.
Roared on by a raucous home crowd, the Cottagers were in command and Juve by comparison looked crestfallen.
Substitute Dempsey entered the fray in the 72nd minute with his side well on top and 10 minutes later he was to deliver the coup de grace.
The United States forward executed an exquisite chip which found the top corner of the net over the head of the back-pedalling Chimenti to send the home fans delirious.
Two-time European champions Juventus were beaten and the late sending off of Jonathan Zebina for a petulant flick at Duff was the last act on a night to forget for the Turin giants.