The Red Devils, who sit 15 points clear of Manchester City at the top of the table, have six fixtures remaining on their calendar - meaning there are 18 points left to play for.
They need to break through the 95-point barrier if they are to re-write the history books, with Chelsea having set the top-flight benchmark back in 2005.
Evra believes United are capable of hitting that target, with Sir Alex Ferguson having drilled into his players the importance of finishing with a flourish, as opposed to stumbling over the line.
Ahead of a trip to West Ham United on Wednesday, the French full-back said in the Manchester Evening News: "The boss is a winner. 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 those remaining games.
"We can still break the record. That is what he wants. He just wants to win game after game.
"The challenge for us is to win the six games that we have left. It won't be easy, but that is the way the boss wants us to play."