Former Republic of Ireland winger Damien Duff, who retired from international football on Friday, scored his second goal of the season to give Fulham a third-minute lead.
But United’s £24m signing Van Persie equalised before Shinji Kagawa and Rafael both netted to leave Sir Alex Ferguson’s side 3-1 ahead at half-time.
David De Gea failed to collect a cross in the 64th minute which led to United captain Nemanja Vidic inadvertently turning the ball into his own net, but the home side hung on to claim three points.
“It is always good on your debut to score a goal like that. I enjoyed it,” Van Persie told BBC Sport.
Martin Jol claims he does not have a problem with star man Clint Dempsey and he still hopes to keep him at Fulham this summer.
The 29-year-old American international has expressed a desire to leave Craven Cottage this summer as he wants to join a bigger Premier League side where he has an opportunity to lift some silverware.Like what the TT have on offer? Sign up for more notifications!