Wayne Rooney paid the price for a below-par performance in the defeat at Everton on Monday, with Van Persie starting as a lone forward in a 4-2-3-1 formation.
United fell behind to Damien Duff's second-minute effort but collected all three points as the first-half response of Van Persie, Kagawa and Rafael proved enough despite a Nemanja Vidic own goal.
In addition to their goals, Van Persie and Kagawa in particular caught the eye with how easily they fitted into the system during the first half, the latter excelling in the hole behind the main striker. His movement, speed and passing kept Fulham on the back foot.
The game started badly for United, however, when Bryan Ruiz rolled a free-kick into Duff's path which the Irishman turned home before guest of honour Usain Bolt had even taken his seat.
Coming so soon after that loss at Everton, it was a major test of character for United which they came through with flying colours.
Van Persie levelled with the clinical efficiency you would expect of a Golden Boot winner.
Meeting Patrice Evra's left-wing cross perfectly, the Dutchman flashed a shot wide of Mark Schwarzer before turning to receive the acclaim of his team-mates.
From that point on it was a case of when, rather than if, the hosts would gain the initiative.
As Kagawa prompted and cajoled, Ashley Young and Antonio Valencia both went close.
But when Van Persie's corner was half-cleared to Tom Cleverley, Schwarzer could only turn the midfielder's shot into the path of Kagawa, who - profiting from Sascha Riether's failure to get out of the six-yard box quickly - swept home from close range.
Restored to the starting line-up following his Olympic campaign with Brazil, Rafael provided additional defensive security.
He also had a goal correctly ruled out for offside before nodding home Young's chip to the far post just before the break.
Yet, for all United's attacking endeavours, there remain serious flaws at the back amid a massive injury list.
Once again pressed into service as an emergency centre-half, Michael Carrick came far too close to turning the ball into his own net for comfort.
And when United conceded a second, it was almost laughable as David de Gea came to punch Matthew Briggs' cross, got nowhere near it and the ball eventually bounced off Vidic and rolled in.
De Gea redeemed himself with two brilliant saves to deny the excellent Mousa Dembele.
And then, on Fulham's last attack, De Gea denied Ruiz, who had been set up by Dembele.
Rooney was introduced for Kagawa for the final 22 minutes but was stretchered off in the closing seconds after suffering a deep gash to the side of his right knee after a clash with Hugo Rodallega.