Marouane Fellaini headed in a corner kick from Darron Gibson in the 57th minute, giving Everton a season-opening 1-0 upset win over Manchester United on Monday night.
After losing the Premier League title to rival Manchester City on goal difference last May on the final day of a trophyless season, United lost at Goodison Park for just the fourth time in 21 Premier League meetings.
"I don't think anybody tonight was considering Everton at all," Everton manager David Moyes told Sky Sports television. "A lot of people forgot Everton aren't a bad team, and Goodison is a difficult place to come and win."
It was the first time United lost a league opener since 2004.
Robin Van Persie, signed from Arsenal on Friday, entered in the 68th minute in his United debut. American goalkeeper Tim Howard got the shutout for Everton, coming off a seventh-place finish.
Tom Cleverley came closest to tying the score, but his shot was cleared off the line by Phil Jagielka midway through the second half.
"It's nice to send the Everton fans on the first day of our season home with a win and not the doom and gloom we normally start with," Jagielka said.
United was playing its first competitive match since becoming a listed company on the New York Stock Exchange.
Manchester United manager Sir Alex Ferguson criticised his own players for failing to utilise Robin van Persie's talents after they crashed to a surprise 1-0 defeat at Everton.
Van Persie made his eagerly-anticipated United debut as a 68th minute substitute with his new side trailing to Marouane Fellaini's second half goal at Goodison Park on Monday.But the Dutch striker, who completed a 24 million pound
move from Arsenal last Friday, was unable to inspire Ferguson's team, who lost their opening game of the Premier League season for the first time since 2004.