Wilson, 18, make his senior bow alongside young Welsh midfielder Tom Lawrence in Tuesday's 3-1 Premier League victory against Steve Bruce's side at Old Trafford.
And the England Under-19 international made the most of his opportunity by scoring a goal in each half before he was replaced by Van Persie.
The Netherlands striker got in on the act with a goal of his own to seal the points four minutes from time after Matt Fryatt had pulled a goal back.
And the former Arsenal captain was hugely impressed by the impact made by Wilson.
He told United's official website: "James played really well.
"I know how hard it is to make your debut - I made mine when I was about 29!
"I know how special it can be. He made it very special for himself and for everyone. To score two goals is really special."
United's victory ensured they can still finish sixth and seal a UEFA Europa League spot if they win at Southampton on Sunday and Tottenham lose at home to Aston Villa.
