Van Persie ended a run of ten games without a goal for Manchester United by netting from the penalty spot against the Potters as his team cruised to a 2-0 victory.
The Dutchman celebrated by running towards the United dugout and embracing manager Sir Alex Ferguson, a move which has earned him plenty of ribbing from the rest of the team, reveals Evra.
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"To be fair, Robin told us he was really emotional. He had not scored for 10 games. He just showed the passion and the way he wanted to win.
"He said to us, 'Hands up guys, it was an emotional game. I did it, it is okay, we can move on now'.
"It was nice. I can see a lot of love and emotion. It is the first time we saw that [from Robin]. It is good to see love like that on the pitch sometimes.
"I always say the atmosphere at this club is great. That is a big strength for Manchester United."
Evra also revealed Sir Alex has challenged his team to finish the season strongly with the Premier League record points total still in sight.
"The boss is a winner," he added. "He has just told us to win the six games that are left. He said before the Stoke game that the season starts now. That shows you the way he wants to win this 20th title.
"He told us not to think about the title, just think about winning these six games. We can still break the record [points total]. That is what he wants.
"The challenge for us is to win the six games we have left. It won't be easy but that is the way the boss wants us to play."