Damien Duff scored after just three minutes as United struggled again in defence following their opening defeat at Everton, but Van Persie drew his new employers level with a brilliant finish after 10 minutes, the former Arsenal captain caressing a volley into the far corner.
With Wayne Rooney unexpectedly dropped to the bench, Shinji Kagawa - a summer recruit from Borussia Dortmund - added a second from close range before the adventurous Rafael made it three with a header to give United a comfortable lead at half time.
Fulham's ongoing endeavour was rewarded when David De Gea failed to deal with a cross from the left and Nemanja Vidic turned the ball into his own net, but while United clung on to record their first win of the season, they lost Rooney to a nasty gash on the leg in a nervy period of injury time.
Rooney's gash - caused in an accidental collision with a Fulham player - led to the England striker being stretchered from the pitch with blood pouring from his leg.
Both club and country will be looking on nervously to see his prognosis, with early reports suggesting that he will be out for at least four weeks.
In the afternoon's other matches Tottenham Hotspur's frustrating start to the season continued when they were held to an entertaining 1-1 draw by West Bromwich Albion at White Hart Lane.
Benoit Assou-Ekotto's deflected strike from range 15 minutes from the end looked to have given them victory until James Morrison's stoppage time header looped high and back down into the net.
Three first-half goals put Everton on their way to a second win in as many games as David Moyes' men saw off Aston Villa 3-1 at Villa Park
Wigan Athletic struck twice in the second-half to condemn Southampton to a 2-0 defeat at St Mary’s, while Norwich City and Queens Park Rangers both collected their first Premier League points of the season after a 1-1 draw at Carrow Road.
In the early kick-off Swansea City sauntered to top spot after two games when exploiting two horrendous errors to beat West Ham 3-0.
Sunderland's match against Reading was postponed as heavy rain rendered the pitch unplayable at the Stadium of Light.
- Wayne Rooney
- Shinji Kagawa