United surrendered a considerable lead towards the end of last season, which ended up costing them the Premier League title as their closest rivals edged them on goal difference.
The Red Devils secured a dramatic 4-3 victory against Newcastle at home on Boxing Day as City went down to defeat at Sunderland the same day - a result which puts the Old Trafford club in charge heading into the New Year.
French defender Evra admitted that he had never seen so many happy players in the changing room following Javier Hernandez's stoppage-time winner.
He told TV channel Canal Plus: "It was a crazy match. For football lovers, it was a great match. In the end, it was such a great release for us.
"I have never seen the players so happy in the changing room this season. At half-time Sir Alex told us if we could win this game, then we would have a big chance to be champions again.
"Remember, we were seven points ahead last term and we lost the Premier League with goal difference. If we do it again this season, Ferguson could sack us all!"