Martin Jol's side responded well in the second half after shipping three goals in the opening 22 minutes, but the damage had already been done with central defenders Philippe Senderos and Fernando Amorebieta looking like they had just been introduced to each other before kick-off.
Rooney played provider on nine minutes with an easy pass under no pressure for Antonio Valencia to convert before Adnan Januzaj picked out Van Persie to smash the second into the net beyond Maarten Stekelenburg after the Dutch striker beat the offside trap.
Fulham were still smarting from what they felt was a foul by Januzaj on Scott Parker in the build-up to that goal when they fell three behind as Rooney converted from close range to hand his side a 3-0 lead. It was more or less game over then.
Substitute Alexander Kacaniklic saw a shot deflect off Rooney to elude David De Gea with United noticeably dropping off the pace, but they could not add to their total despite the visitors' general sloppiness after half-time.
United were forced to make three changes at the break due to injury that hardly contributed to their overall outlook in the second half. Rafael, Tom Cleverley and Jonny Evans all failed to reappear for the second half with Chris Smalling, Marouane Fellaini and Shinji Kagawa introduced.
9' -VALENCIA OPENS SCORING: Valencia scores from the Rooney pass. So, so easy for United. The visitors with a 1-0 lead.
20' - VAN PERSIE NETS: Van Persie beats the offside trap to smash the ball into the net. Adnan Januzaj with the pass. Maarten Stekelenburg left with no chance.
22' - ROONEY ON THE MARK: All too easy for United as Rooney taps home the Van Persie pass with Fulham ripped to shreds once again. A long old afternoon this one for Fulham.
65' - FULHAM CONSOLATION: Kacaniklic sees a shot deflect off Rooney before nestling in the net. No chance for De Gea. Suddenly 3-1 here in favour of United.
86' - RICHARDSON NODS WIDE: Richardson glances a header wide of the goal from the Kacaniklic cross. Fulham have had chances in this second period.
90+1' - RIETHER STAMP: A clear stamp by Riether on Adnan Januzaj. Riether fortunate to avoid a straight red card for that challenge.
Alex Kacaniklic scored his first Premier League home goal since scoring in the 5-0 home win v Norwich in August 2012. He is yet to finish on the losing side in the previous five Premier League matches in which he has scored (four wins).
Robin van Persie’s goal put him clear as the highest-ever Dutch goalscorer in the Premier League (128), overtaking Jimmy Floyd Hasselbaink on 127, and put him outright 10th in the all-time scorers in the division.
Robin van Persie scored his seventh Premier League career goal in 14 appearances against Fulham.
The previous time Manchester Utd were 3-0 up after 23 mins in a Premier League game prior to today was their 5-1 home win v today’s opponents Fulham, August 20th 2006.
TALKING POINT: How much pressure is Martin Jol under? Fair to say these are not great moments for the Fulham manager, but at least his side showed signs of a recovery with their performance in the second period. Needs to start picking up points. And soon.
MAN OF THE MATCH
Fulham: Stekelenburg 6, Riether 4, Senderos 4, Amorebieta 4, Richardson 5, Dejagah 5, Sidwell 5, Parker 5, Kasami 5, Ruiz 5, Berbatov 5. Subs: Kacaniklic 6, Taarabt 6, Bent 6.
Manchester United: De Gea 7, Rafael 6, Vidic 6, Evans 6, Evra 6, Valencia 7, Jones 6, Cleverley 6, Janzuaj 6, Rooney 7, Van Persie 7. Subs: Smalling 6, Fellaini 6, Kagawa 6.
THE MATCH IN A TWEET