England coach Fabio Capello was in attendance at Old Trafford and showed his appreciation for Rooney's brilliance by applauding his England striker when he was substituted with 20 minutes left.
United left Cristiano Ronaldo and Ryan Giggs out of their line-up, while Arsenal kept Emmanuel Adebayor and Mathieu Flamini on the bench - and the Gunners suffered most from the changes.
Rooney returned from suspension after missing the defeat to Manchester City - and made up for lost time by destroying Arsenal with a blistering first-half display.
He was on the mark after 16 minutes when a Nani corner was only half-cleared, and when Anderson headed the ball back into the danger area Rooney was perfectly placed to divert a close-range finish past Jens Lehmann.
Fletcher deservedly doubled the lead four minutes later when Nani opened up Arsenal on the left flank and crossed for the Scot to head in at the near post.
Rooney continued to terrorise the Arsenal defence and could have added to his goals tally before United made it three seven minutes before the interval.
Carrick split the Arsenal defence wide open, leaving Nani to control and calmly shoot past Lehmann.
Rooney had already tested Lehmann again before Arsenal's misery increased after 48 minutes when Eboue was rightly sent off for a raised boot in a tackle on Evra.
The Arsenal defender seemed reluctant to leave the pitch after referee Alan Wiley brandished the red card, but he had no excuses because it was an horrendous challenge.
Rooney was in almost unstoppable form, tearing the Arsenal defence apart almost at will, shooting wide after beating Kolo Toure and then bringing a fine save from Lehmann - all in the space of seconds.
And with 16 minutes left, United got the fourth goal their dazzling football deserved when Nani floated up a perfect far post cross for Fletcher to head in at the far post.
Arsenal, who have enjoyed taunting outclassed teams in the past, were not enjoying getting a taste of their own medicine and William Gallas was lucky to escape punishment for an ill-disciplined kick at Nani.
Substitute Louis Saha almost added a fifth with two minutes left but keeper Lehmann - who had been blameless in the defeat - saved well again.
Man Utd: Van der Sar, Brown, Ferdinand, Vidic, Evra, Fletcher, Carrick, Anderson (Scholes 72), Park, Rooney (Saha 71), Nani. Subs Not Used: Kuszczak, O'Shea, Tevez.
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