United boss Sir Alex Ferguson rested Wayne Rooney and Cristiano Ronaldo ahead of Tuesday's crunch Champions League tie against Lyon, and his side were rarely tested by a team they have now beaten on their last seven meetings.
Former Fulham striker Louis Saha benefited from Ferguson 's rotation policy with a rare start but wasted a glorious opportunity after only four minutes as he sliced wide after Paul Scholes' chipped pass had put him clean through on Antti Niemi.
Fulham responded immediately though in what was a stunningly high-tempo start to the game as Danny Murphy brought the best out of Edwin Van der Sar with a dipping, swerving volley from 25 yards that was destined for the bottom corner.
But on 15 minutes the visitors took the lead as Hargreaves scored his first goal in English football following his summer move from Bayern Munich.
It was a stunning free-kick from the midfielder, who was given his chance on the edge of the the penalty area after Brede Hangeland had fouled Carlos Tevez and his curling effort sailed past Niemi and into the corner.
United looked set to take full control with Nani to the fore, but Fulham refused to be cowed and Murphy brought a second save out of Van der Sar with a downward header from Jimmy Bullard's free-kick that ought to have been better placed.
But with the game evenly poised, the visitors produced a killer thrust moments before the break as Scholes' delicious cross picked out Park, who could barely miss after being left with acres of space on the edge of the six-yard box.
The gulf in class between the sides was made apparent with 20 minutes left as the visitors were able to bring on Rooney and Ronaldo having given them a rest ahead of the clash with Lyon.
And within two minutes it was 3-0 as John O'Shea escaped down the right before pulling the ball back towards a waiting Rooney.
However, the recovering Davies got there first and only succeeded in diverting the ball inside Niemi's near post for the most unfortunate of own goals that seems to sum up Fulham's fortunes at present, with the hosts now six points from safety.