On that occasion, a victory would have almost certainly secured a 20th Premier League title, but the Reds threw away a 4-2 lead in the dying stages of the game to come away with only a point.
And although United are currently flying high, on a 13-game unbeaten run in all competitions, the United manager says the Reds can expect a similarly tough encounter this weekend.
"It's a tough game on Sunday," Sir Alex said at his pre-match press conference. "We were 4-2 up with seven or eight minutes to go. It was unexpected and we have to anticipate the unexpected in the run-in. That was a bad blow for us and it cost us the league.
"Everton are very experienced and, if you look at their record, they’ve only lost three games this season [the same number as United]. They're obviously hard to beat.
"But the team is playing well, I’m pleased with their form and I’m pleased that the players we’re changing around, when I’m making different team selections, are buying into it well.
"They’re all contributing in their own way and that gives us a better chance in terms of dealing with the various competitions we’re in now."
United began the 2012/13 season with defeat away at Everton, on a night in which Toffees target man Marouane Fellaini caused the Reds' defensive line untold problems. Full-back Leighton Baines has also drawn widespread praise this term for his performances.