Five of the goals came in a frantic first half which confirmed the strengths and weaknesses of both sides.
United, superb in attack and down the flanks, lacked power in midfield.
Since Sir Alex Ferguson took his side's January spending to £12.5 million on defenders Patrice Evra and Nemanja Vidic they have leaked six goals in four days.
Evra, who was replaced after 79 minutes had a nightmare game, while Vidic, a replacement for Gary Neville with 21 minutes to go made little impact.
Fulham, who are yet to win away in the league this season, were vibrant in midfield and up front, but defensively, were venerable both from pace and in their marking.
United opened the scoring from a fortuitous sixth-minute goal. Neville's cross from the right was hit straight back to him by Wayne Bridge. The second cross found Ji-Sung Park and the South Korean scored his first Premiership goal for United with a right-foot shot from 12 yards which took a deflection off Fulham's Carlos Bocanegra on its way past goalkeeper Antti Niemi.
United's second goal eight minutes later came from a superb piece of individual skill from Cristiano Ronaldo.
Fulham debutant Michael Brown, a £1.75 million signing from Spurs, fouled Louis Saha 30 yards from goal. Ronaldo stepped up to curl his glorious right-foot free-kick flying past the bemused Niemi and into the roof of the net.
But the Cottagers showed great character when they stormed back to reduce the arrears in the 22nd minute. Liam Rosenior's cross from the right found Brian McBride leaping above Neville to head home from seven yards.
Back came United to make it 3-1 a minute later. Saha cut in from the left, but when he found Ruud van Nistelrooy just inside the Fulham box, the Dutchman was clearly offside.
Play was allowed to continue and, although Niemi saved van Nistelrooy's shot, Saha followed up to score with a close-range tap-in against his former club.
Fulham boss Chris Coleman's protests saw him sent to the stands by referee Martin Atkinson.
United's defensive frailties were there for all to see again in the 36th minute.
Bridge beat off Park's challenge as he raced down the left. His cross to the far post from the byline was met by Heidar Helguson leaping high above Evra to head home from six yards - United goalkeeper Edwin Van der Sar parrying the ball into his own net against his former club.
United's defence, shaky in the first half, became shambolic in the second. The farce was encapsulated in Evra's aerial collision with Mikael Silvestre when they went for the same ball.
The hosts held on and clinched victory five minutes from the end with another superb goal.
Van Nistelrooy released Saha down the left and his cross set up the Dutchman to fire in a shot from the edge of the box.
Niemi clawed the ball away but Ronaldo reacted quickly to get in a shot from the right byline which hit the far post and rolled over the line and into the back of the net.