For 80 minutes, Fulham didn't even manage a shot on target and it looked as though it was going to be a stroll in the sunshine for Sir Alex Ferguson's men.
But an astonishing last ten minutes saw United almost pay for their complacency. In the 81st minute Lee Clark's shot from just inside the United penalty area hit the post with Tim Howard beaten.
The rebound fell to Carlos Bocanegra on the left side of the United box but this time the United keeper proved to be the hero when he made a superb acrobatic save to claw away the Fulham defender's shot.
United's failure to comprehend the danger gave Bocanegra a follow-up shot which hit team-mate Steed Malbranque who was standing four yards away from the line.
It was a warning for United which they failed to heed. With the game moving into injury time, Fulham's former United hero Andy Cole beat Rio Ferdinand on the right side of the box only to see his eight-yard shot superbly saved by Howard with his legs.
Then in the dying seconds Liam Rosenior crossed from the right and substitute Tomasz Radzinski, standing unmarked eight yards out, failed to control the ball.
It was a nervous finale which United should never have had to endure - and one entirely of their own making.
The first half was a United lesson in how to dominate your opponents without killing them off. Fulham had no answer to the trickery of Cristiano Ronaldo as United fed him at will.
In the seventh minute, the Portuguese winger headed narrowly wide at the near post from Quinton Fortune's inswinging corner. Seconds later, Ruud van Nistelrooy won his tackle with Papa Bouba Diop in the centre circle and sent Ronaldo clear down the left.
Ronaldo provided the perfect cross from the edge of the box but Wayne Rooney's six-yard flick flew narrowly wide before the excellent Edwin Van der Sar tipped Roy Keane's fierce 25-yard effort away.
Fortune's cross from the left then saw Paul Scholes plant a clever ten-yard header narrowly wide of the near post.
Gabriel Heinze fizzed a vicious dipping left-foot volley just over the bar before United broke the deadlock in the 21st minute.
Neat passing between Scholes and Rooney found Keane, whose glorious pass sent Ronaldo away down the left. The twinkle-toed teenager cut across the Fulham box before smashing a glorious right-foot shot into the roof of the net.
United could have easily tied up the points by the interval. Mikael Silvestre's long pass out of defence found Ronaldo in the penalty area and, with Alain Goma at his back, he still managed to get in a shot which was taken by the diving Van der Sar.
Ferdinand's raking 50-yard pass then found Keane on the left and his ball inside set up Heinze whose shot was deflected narrowly wide. The second half started as the first had finished and Van der Sar was at full stretch to take Rooney's powerful cross-shot from the right byline.
In the 59th minute Fortune teed up Rooney who hit a powerful 25-yard drive which was well-saved by Van der Sar. Ronaldo then curled another shot just wide and Rosenior almost deflected the ball into his own net when he got in the way of another fierce Rooney shot.
Scholes' clever pass sent Ronaldo racing away down the left and he curled another shot from the edge of the box narrowly wide. Van de Sar managed to get a fist to a wickedly bouncing left-wing cross from Heinze as van Nistelrooy stole in at the far post and the Argentinian tested the Fulham goalkeeper with a 20-yard shot soon after.
United were coasting to three points when Fulham suddenly came to life as they almost provided a sting the tail.
But, despite the Londoners' late fling, United still had chances to score that vital second goal. The arrival of Alan Smith as a substitute for the out-of-sorts van Nistelrooy posed United's late threat.
A superb one-two between Smith and Ronaldo almost ended with a goal but Van de Sar blocked Smith's powerful shot.
Unfortunately for United, the ball hit Scholes and rebounded back in to the Fulham keeper's arms.
Van der Sar produced another brilliant save three minutes from time when Scholes found Ronaldo on the right. His cross to the near post saw substitute John O'Shea connect with a fierce eight-yard shot which was superbly turned behind by the keeper.
When Van de Sar pressed forward in injury time, Smith almost scored with an audacious lob from the halfway line, but the Dutch number one managed to get back just in time to collect the ball on his line.
MAN OF THE MATCH: Cristiano Ronaldo (Manchester United) - Scored a superb goal and produced a dazzling display of wing play. Fulham had no answer to his bewitching individual performance – one of his best of the season.