Fulham struggled in the first half at the Stadio Olimpico and conceded twice to goals from Nicola Legrottaglie and Jonathan Zebina.
Dickson Etuhu pulled one back for Fulham but David Trezeguet's third goal just before halftime emphasised the gulf in class between the two sides.
The bookmakers have Juve their favourites to go on and lift the trophy - at a best price of 7/1 before the night's action. Fulham are out at 66s.
Liverpool had begun the day as the tournament favourites but they've drifted after slipping to a 1-0 defeat at Lille (20s).
Hamburg are at 10/1 after a 3-1 win against Anderlecht, with Valencia and Marseille also in the top six options after draws with Werder Bremen and Benfica respectively.
Top Ten Outright Winner Prices for the Europa LeagueJuventus 8.00 @ Centrebet
Liverpool 8.80 @ Betfair
Valencia CF 11.00 @ Paddy Power
Hamburger SV 11.00 @ Centrebet
Olympique Marseille 15.00 @ Centrebet
SL Benfica 15.00 @ Paddy Power
SV Werder Bremen 15.00 @ Bodog
Atletico Madrid 17.00 @ Betfred
VfL Wolfsburg 17.00 @ Bet365
FK Rubin Kazan 24.00 @ Betfair