Van Persie struck the only goal of the game last night.
And with the championship already looking like a two-horse race as Chelsea crumble, Allardyce thinks Van Persie could be a decisive factor.
"Manchester United have lots of players who will have good spells and can come up trumps when they need them to," said Allardyce.
"Robin van Persie is a quality player and we have largely kept him quiet.
"But he will score 20 goals for Manchester United, maybe 30. In the end that is normally the difference."