Sir Alex Ferguson responded to his side's loss to Everton last week by dropping Wayne Rooney to the bench at the expense of Van Persie, but Fulham took a third-minute lead through Damien Duff.
United were level in the 10th minute and almost inevitably it was Van Persie with the strike, the Dutchman stealing in front of Brede Hangeland to curl home a brilliant first-time effort.
Kagawa popped up with his first goal since arriving from Borussia Dortmund to hand United a 35th-minute lead before full-back Rafael made it three when he nodded home in the 41st minute.
Fulham pulled one back in the 64th minute after a mix-up saw United goalkeeper David De Gea bundled over by Nemanja Vidic as both players looked to deal with a cross under pressure by Mladen Petric, the ball flicking off the Serbian defender before bouncing into the net.
Rooney eventually made his entrance as a 68th-minute substitute, but the England striker's afternoon ended on a sour note when he was taken off on a stretcher with a nasty puncture wound to his thigh after a challenge with Hugo Rodallega.
In the day's early game, Swansea's bright start to the campaign continued with a 3-0 victory over West Ham.
Michael Laudrup's side looked superb going forward as they swept aside QPR 5-0 on the opening day of the season and they were similarly lethal at the Liberty Stadium as goals from Angel Rangel, Michu and Danny Graham sealed another eye-catching victory.
Aston Villa's unconvincing start under Paul Lambert continued, however, as they lost 3-1 to Everton at Villa Park.
The visitors took the lead in the third minute as Steven Pienaar lashed home from 20 yards.
It was 2-0 in the 31st minute when Marouane Fellaini followed up his winner against Manchester United with another headed effort, although Villa goalkeeper Shay Given should have made a routine save.
Nikica Jelavic made it three from Leighton Baines' pull-back on the stroke of half-time, and Villa's afternoon took a further nosedive in the 58th minute when Ciaran Clark was shown a straight red card for a professional foul on Jelavic.
The hosts pulled a goal back through new signing Karim El Ahmadi in the 74th minute, but it was too little, too late.
At White Hart Lane, Andre Villas-Boas was denied his first win as Tottenham boss in dramatic fashion as James Morrison struck late to secure a 1-1 draw for West Brom.
Benoit Assou-Ekotto opened the scoring for the hosts in the 74th minute, the full-back lashing home a deflected effort after the Baggies failed to clear their lines from a corner.
Spurs looked like they had done enough to claim the victory but Morrison popped up in the first minute of stoppage time to fire in a low effort.
Wigan picked up their first win of the season as they eased to a 2-0 victory at Southampton.
The Latics took the lead six minutes into the second period when Franco Di Santo was played in by Shaun Maloney and the striker finished emphatically beyond Kelvin Davis.
New signing Arouna Kone made it two in the final minute, the former Sevilla striker stealing the ball from Jose Fonte near the halfway line and then being allowed the freedom of St Mary's to run in and score.
Norwich and QPR recovered from heavy opening-day losses to share a 1-1 draw at Carrow Road.
Simeon Jackson's close-range header gave Norwich an 11th-minute lead, but the visitors were level in the 19th when Djibril Cisse went down under a challenge from Canaries new boy Sebastien Bassong and referee Mark Clattenburg pointed to the spot.
Cisse's low penalty was saved by John Ruddy but when the ball came back off the post it broke to Bobby Zamora who had a simple task to find the bottom corner.
Sunderland and Reading's game at the Stadium of Light was postponed due to a waterlogged pitch.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!