Ruud van Nistelrooy scored his 100th and 101st goals for Manchester United, who survived a superb Everton comeback.
Trailing 3-0 at half-time courtesy of two goals by Louis Saha and Van Nistelrooy's strike, Everton took the game to United after the break.
David Unsworth headed the hosts' first, John O'Shea scored an own-goal and Kevin Kilbane blazed in the equaliser.
But a glancing header by Van Nistelrooy from Ronaldo's cross in the dying minutes gave United all three points.
9 mins: Saha fires Man Utd into the lead
24 mins: Van Nistelrooy fires in United's second
29 mins: Saha nets United's third
49 mins: Unsworth heads home Everton's first
65 mins: O'Shea own-goal gives Everton hope
75 mins: Kilbane grabs the equaliser for Everton
89 mins: Van Nistelrooy snatches the winner for United
United signalled their intent from the outset, attacking the Everton defence with vigour.
Paul Scholes was buzzing around the midfield and drove forward with purpose to almost give United the lead.
The England international unleashed a powerful shot from 20 yards that crashed off the post.
Van Nistelrooy was well placed to bang home the rebound, but the Dutchman somehow contrived to balloon the ball over the bar.
That was a lucky escape for Everton, who looked sluggish despite the changes manager David Moyes had made to his side.
Duncan Ferguson and Francis Jeffers were brought into the attack, with Wayne Rooney left on the bench.
But it was the hosts' defence that was giving cause for concern as they failed to cut out Darren Fletcher's crosses from the right.
Saha should have done better moments after Scholes' effort, but the Frenchman could not direct his header on target.
Yet Saha was given the chance to make it two goals in two starts for United when he ran onto Mikael Silvestre's through-ball and thumped home the opener from 18 yards out.
Everton's defence had been caught completely square and could do nothing to prevent Saha's superb start to his United career.
Saha makes it three goals in two starts for United
But just as Everton were getting back into the game, United doubled their lead through Van Nistelrooy.
Everton were again undone by poor defending, leaving Van Nistelrooy to run into the area and clinically despatched his 100th goal for United from six yards out.
There was no let-up for the hosts and the magnificent Scholes set up Saha for his second of the afternoon.
Saha and Van Nistelrooy were simply breathtaking, and the pair certainly look as though they will strike up a formidable partnership.
Both had chances to add to their tallies, but fluffed their lines at the crucial moment.
Such was the poverty of Everton's first-half performance, that United would not have been flattered by a 7-0 scoreline.
Rooney, Tomasz Radzinski and Gary Naysmith were introduced after the interval as Everton looked to restore some pride.
And Unsworth reduced the deficit by steaming in at the far post to head home Naysmith's corner.
The presence of Naysmith and the prodigious Rooney lifted Everton, and he forced the corner which led to a scrambled second, the ball bouncing off O'Shea for an own-goal.
Ferguson went agonisingly close to heading an equaliser, but Everton were not to be deterred.
The home side launched attack after attack and they were rewarded for their endeavour when Kilbane struck the equaliser from Thomas Gravesen's free-kick.
The in-form Nigel Martyn made a superb save to deny Scholes in the dying stages, but he could do nothing to stop Van Nistelrooy's glancing header.
Rooney then missed a glorious chance to level the game once more in what would have been a fitting finish to a breathtaking encounter.
Everton: Martyn, Hibbert, Stubbs, Unsworth,
Pistone (Naysmith 45), Watson (Rooney 45), Gravesen, Carsley, Kilbane, Ferguson, Jeffers (Radzinski 45).
Subs Not Used: Simonsen, Linderoth.
Man Utd: Howard, Gary Neville, Brown, Silvestre, O'Shea, Fletcher (Ronaldo 80), Keane, Scholes, Giggs, Saha (Fortune 73), van Nistelrooy.
Subs Not Used: Butt, Carroll, Kleberson.
Referee: N Barry (N Lincolnshire).