The Australian stopper performed first-half heroics for the swamped visitors, repeatedly denying Rooney and Nani, while the Cottagers' only other consolation was a late header from Hughes.
Sir Alex Ferguson made just three changes to the side which edged through the Reds’ third round replay with West Ham, replacing Anders Lindegaard, Alexander Büttner and Antonio Valencia with David De Gea, Patrice Evra and Michael Carrick respectively.
Wayne Rooney proved United’s match-winner with an early goal against the Hammers, and the England striker almost repeated the feat inside a minute after sloppy play from Steve Sidwell.
The Cottagers midfielder’s sloppy pass went straight to Rooney, who bore down on goal before having his initial effort blocked by Brede Hangeland, then Sidwell atoned by deflecting Rooney’s follow-up into the side netting.
Fulham’s reprieve was only brief, however, as the subsequent corner led to the opening goal. Rooney’s in-swinging cross was inexplicably flicked away from Chris Smalling by Aaron Hughes, and referee Mark Clattenburg had little option but to award a penalty.