New signing Bobby Zamora opened his account by giving Fulham a 2-0 lead just past the half-hour mark.
The Scottish Premier League titke holders reduced the deficit just three minutes before half time from a superb Barry Robson free-kick.
Substitute Leon Andreasen sealed victory for Fulham with a third goal just five minutes from the final whistle.
Fulham: Stockdale, Konchesky, Pantsil, Hangeland, Andranik, Nevland, Gera, Aaron Hughes, Bullard, Davies, Zamora Subs: Etheridge, Volz, Seol Ki-Hyeon, Healy, Murphy, Johnson, Cook, Dempsey, Andreasen, Kallio.
Celtic: Mark Brown, Andreas Hinkel, Lee Naylor, Stephen McManus, Gary Caldwell, Scott MacDonald, Scott Brown, Massimo Donati, Barrry Robson, Chris Killen, Aiden McGeady Subs: Scott Fox, Bobo Balde, Georgios Samaras, Paul Hartley, Mark Wilso, Shinsuke Nakamura, Cillian Sheridan, Koki Mizuno Darren O'Dea, Paul Caddis, Paul McGowan.