United's new recruit Louis Saha is paying an immediate return on the club's investment and his first-half brace, allied to a van Nistelrooy goal, had the visitors in command.
But a stunning second-half fightback from Everton, which delivered goals from David Unsworth, a John O'Shea own goal and Kevin Kilbane, seemingly earned the hosts a point until van Nistelrooy headed a dramatic winner two minutes from time
The visitors completely controlled the first period and Everton could have had no complaints had the 3-0 advantage been double such was the ineptitude of their defence.
United should have been ahead just two minutes in when Paul Scholes' shot cannoned off the post to van Nistelrooy but the Dutch hot shot miscued his effort with the goal at his mercy.
Saha also missed an early opportunity when he glanced Darren Fletcher's cross wide but there was no mistaking the clinical nature of his finishing after nine minutes.
Mikael Silvestre's long ball forward sprang Saha clear of the Everton rearguard, which was vainly appealing for offside, and the Frenchman composed himself before firing an unerring shot beyond Nigel Martyn.
Lee Carsley shot straight at Tim Howard while the Everton fans thought they had equalised on 21 minutes but Thomas Gravesen's shot only rippled the side-netting.
Van Nistelrooy poached his landmark goal on 24 minutes when Saha's pass was diverted in to the box by Carsley and, with Alan Stubbs unable to win the ball, the Red Devils ace tucked his shot under Martyn.
Howard fumbled a Francis Jeffers shot as Everton sought a riposte but they fell further behind just before the half-hour mark when a neat passing move culminated in Scholes picking out Saha for the striker to drill past Martyn.
Saha should have grabbed his hat-trick when latching on to another Scholes pass but blazed his shot off target while van Nistelrooy dragged an attempt wide after racing clear of the home defence.
But the half time introduction of three fresh faces by David Moyes proved to be the catalyst for a quite amazing turnaround in the contest.
Everton hauled themselves back in to the game four minutes after the break when substitute Gary Naysmith's corner brushed off O'Shea, who had needlessly conceded the set piece, to the far post where Unsworth stooped low to head in.
Another replacement, Wayne Rooney, was tormenting the visiting defence and he was twice thwarted by Howard, with the latter save the forerunner to Everton's second goal.
Howard smartly pushed Rooney's shot away for a corner and, from Naysmith's resulting set piece, O'Shea headed in to his own net under pressure from Ferguson.
Rooney almost levelled matters when pinching the ball off Wes Brown but Howard scrambled back to block the England international's shot.
Everton made United pay the price for their slack second-half display when they capped their remarkable comeback with 15 minutes remaining.
Fletcher's untimely foul on Kilbane presented Gravesen with the chance to whip in a dangerous free kick, which was powerfully headed home by the Republic of Ireland midfielder, who had not been picked up by United's static back-line.
United were then faced with the task of attempting to win a game they had in the bag, with Martyn producing an excellent low save to keep out Scholes' well-struck shot.
The Red Devils got themselves out of jail with two minutes remaining when substitute Cristiano Ronaldo curled in a magnificent cross to the far post for ace poacher van Nistelrooy to head home and spare the champions' blushes.
