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The World Cup star opened his account in the 12th minute, finishing off a one-two with Facundo Sava.
Steve Marlet came close to extending the lead after 20 minutes but his header was kept out by Bolognia keeper Pagliuca.
Tomas Locatelli levelled matters for the Italians before half time, his long range shot finding the bottom corner of Edwin van der Sar's net courtesy of a Zac Knight deflection.
Inamoto put The Cottagers into an early second-half lead, cutting in to unleash an unstoppable volley past Pagliuca.
Then, just after after Marlet had struck the bar, the Japanese star capped a memorable night by completing his hat-trick.
A Marlet cross fell nicely for Inamoto who struck only to see his shot rebound back and he made no mistake with the rebound from a tricky angle.
And so, Fulham can now look forward to taking their rightful place in the UEFA Cup draw later this week.
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Fulham: Van der Sar, Finnan, Brevett, Knight, Goma, Inamoto, Marlet, Legwinski, Sava, Davis, Boa Morte.
Subs: Taylor, Collins, Melville, Hayles, Malbranque, Ouaddou, Saha.
Bologna: Pagliuca, Zaccardo, Olive, Castellini, Nervo, Colucci, Cruz, Signori, Falcone, Locatelli, Paramatti.
Subs: Coppola, Gamberini, Bellucci, Smit, Goretti, Frara, Meghni.
Referee: Massimo Busacca (Switzerland).
Attendance: 14,756