The Netherlands striker has been in sensational scoring form following his £24 million move from the Gunners, firing the club to the top of the league, and Evra sees similarities between him and former star Van Nistelrooy.
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"He has started so well and I just hope he can keep going because, at United, you have to do that in every game and we have to do everything we can to make sure he feels good.
"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 Van Nistelrooy.
"First of all, they are both Dutch! But it's the class and the touch they both have when you pass the ball to them.
"I played with Ruud when I signed for United and remember what a great player he was.
"I hope he can keep going because he can be one of the best."
Van Persie endured a tough reception from Arsenal fans but had the quality needed to silence them early on in the game as he capitalised on a poor clearance from Thomas Vermaelen to open the scoring, and Evra was impressed.
He added: "Everyone knows what a great player he was at Arsenal, but it is never easy to play against your old team-mates.
"We were not concerned with his attitude as he is a great professional and a great player. After two minutes, though, he scored a goal and it was a great start for him and for us."