Ronaldo and Rooney were rested in readiness for the Champions League clash with Lyon at Old Trafford on Tuesday - but it did little to disturb United's rhythm in a first 45 minutes they dominated with embarrassing ease.
Louis Saha should have put United ahead after only five minutes when he was sent clear by a raking Scholes pass, but he was hopelessly off target with only Fulham keeper Antti Niemi to beat.
It was only a matter of time before United took the lead, and so it proved on 15 minutes when Brede Hangeland fouled Carlos Tevez and Hargreaves clipped a clever free-kick past Niemi from 20 yards.
Nani then shot narrowly wide and Scholes saw a header well saved by Niemi as United threatened to over-run Roy Hodgson's troubled side.
United's failure to take their chances almost cost them 12 minutes before the interval when Danny Murphy escaped his markers but saw a point-blank header blocked by Edwin van der Sar.
The champions doubled their advantage on the stroke of half-time when Park met Scholes' cross with a firm header to leave Fulham facing a mammoth task.
Fulham made little or no impact in the early stages of the second half, and United demonstrated their squad strength after 68 minutes, sending on Rooney and Ronaldo for Tevez and Saha.
United were still in the ascendancy and Niemi had to be sharp to save low down from Park as he drove into the danger zone.
The game was finished as a contest with 18 minutes left when Davies unluckily diverted O'Shea's shot past Niemi at the near post for United's third.
Fulham boss Roy Hodgson: "I don't think five wins from our last 10 games is an impossible task, It's a big task but not impossible.
"Manchester United have a wealth of talent. 3-0 sounds like we've been outplayed but I don't think that was the case. We were not outclassed.
"For me it is simply back to work but not back to the drawing board."
Manchester United manager Sir Alex Ferguson on the title race: "It's been a see-saw and now it is down to one point but Chelsea are still right on our coat-tails.
"It looks as if it is going to be a fantastic run-in.
"I didn't think it was a great game at Fulham. It was a very windy day and a lively pitch but I think we did the job very professionally."
Man Utd: Van der Sar, Evra, Ferdinand, Brown, O'Shea, Nani (Anderson 75), Scholes, Hargreaves, Park, Tevez (Ronaldo 69), Saha (Rooney 69). Subs Not Used: Kuszczak, Pique.
Goals: Hargreaves 15, Park 44, Davies 72 og.
Att: 25,314
Ref: Mike Dean (Wirral).
BBC Sport Player Rater man of the match: Manchester United's Owen Hargreaves 7.90 (on 90 minutes).
• Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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