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.
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.
"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.
