Van Persie scored his 10th goal in 13 games for the Red Devils as they overcame Arsenal 2-1 on Saturday.
After the match, Evra said: "Everyone knows what a great player he was at Arsenal, but it is never easy to play against your old teammates.
"People can now see that Robin is strong mentally. He seems like he has played for us for many years and he reminds me of Ruud van Nistelrooy. I hope he can keep going because he can be one of the best, just like Ruud.
"I played with Ruud when I signed for United and I remember what a great player he was. They are both Dutch but it's more than that. They have the same class and touch when you pass the ball to them."
Van Nistelrooy scored 150 goals in 219 appearances for United between 2001 and 2006.