Alexander Kacaniklic's deflected strike after the restart reduced the arrears, but United saw out the remaining few minutes to secure the victory.
Below, Sports Mole has looked back over the 90 minutes to determine if the result was a fair one.
On target 4
On target 6
Was the result fair?
An unequivocal yes! Fulham struggled to claim a foothold in proceedings during the first 45 minutes as United threatened to win by a cricket score. The second half was much more of an even contest, but the damage had long been done by then.
Where does manager Martin Jol go from here? People will say that there were positives to take from the second-half performance and perhaps they have a point, but that was against a United side that were in cruise control by then. While Jol can no doubt have accepted that his team would be outclassed by the visitors, the lack of desire and effort shown by some players during the opening 45 minutes was extremely worrying. Had United continued their dominance after the restart, then it could have been embarrassing for the hosts.
Man United's performance
The first 45 minutes was the sort of display that Moyes must have craved since he took charge in the summer. They were fluent in their passing and the movement in the final third of the pitch was slick. The Scot is likely to be equally, if not more, pleased with his defence, who with Nemanja Vidic back from injury, looked much more of a solid unit. They may have taken their foot of the gas somewhat after the restart, but they rarely looked in danger of surrendering their advantage.
Sports Mole's man of the match
Wayne Rooney: Whatever Moyes said to Rooney during the summer has certainly done the trick. The United frontman has a new lease of life under the former Everton manager and it is showing in his performance on the field of play. He was at the centre of everything that was good about United today. His awareness to set up Valencia for the game's opening goal was extremely clever, while he also got his name among the scorers.
Kieran Richardson has never been known for his goalscoring credentials and he did nothing to alter that viewpoint this afternoon. With his side trailing 3-1 in the closing stages, he had a very good chance to reduce the arrears, but his header from just six yards out flew well wide of the target.
It was a relatively quiet encounter for Lee Probert to officiate, but to be fair to the referee, he did not create himself any extra work by blowing up for needless fouls and stoppages. He only issued the yellow card three times and on each occasion the offence warranted that punishment.
Fulham: Next weekend Fulham travel to Merseyside where they will face Liverpool at Anfield.
Man United: Attention turns to European football during the week as United make the trip to Spain to face Real Sociedad.