The Frenchman has warned his team-mates that the Gunners have nothing to lose, and admits that there will be a lot of pressure on his own side if they do not win
The two sides play each other at the Emirates Stadium on Sunday, with the Gunners having a near impossible task of overturning a nine-point deficit in the remaining four Premier League games.
But the Frenchman has warned that the north London outfit could take their frustration out on the Red Devils.
"You have to fear the wounded animal," Evra told reporters. "It is all or nothing for Arsenal so that is a danger.
"They will want to show they can still win the title."
United have lost only twice in their last eight league visits to take on Arsene Wenger's men, and Evra said: "We have a good record at Arsenal but statistics can change so quickly.
"Everyone used to say how Arsenal kept losing to Chelsea and then they beat them. We kept losing at Stamford Bridge but won there in the Champions League
"Our record at the Emirates will hurt them and they will want to do something about it."
A defeat at the hands of the Gunners could potentially allow Chelsea to come back in with a serious chance to win the title, as the two teams are set to play each other before the end of the season.
"Sunday is a massive game for us. It is a great opportunity," Evra added.
"There is still a lot of pressure on us.
"If we lose and Chelsea have beaten Tottenham on Saturday, they will only be three points behind and they have to come to Manchester.
"That is what we have to think about now."