Premier League leaders United were on course to go eight points clear of Manchester City before the second-placed side kicked off away to bottom of the table Wolves later on Sunday.
But instead this match ended all square and with the title race in the balance once again.
Two goals for Wayne Rooney and further efforts from Danny Welbeck and Nani had put United in front at 3-1 and 4-2 but Nikica Jelavic, who had scored the first of the days eight goals, made it 4-3 eight minutes from time and Steven Pienaar capped an incredible afternoon with an 85th minute equaliser.
United appeared to have taken control with a second half spell that featured three goals in 13 minutes -- including a response from Everton's Marouane Fellaini.
Nani made the first of those goals after 56 minutes, winning an aerial challenge and squaring to Welbeck on the edge of the Everton penalty area.
The forward neatly side-stepped John Heitinga before placing an unstoppable shot past former United keeper Tim Howard from 17 yards.
The relief around Old Trafford was obvious and, suitably buoyed by the goal, United clicked up through their attacking gears with Nani making it 3-1 after an hour. The Portuguese winger played a short pass to Michael Carrick who, in turn played in Welbeck.
The striker's quick-thinking saw him move the ball on to Nani who chipped the ball over the advancing Howard from six yards.
However, Fellaini's 67th minute goal gave Everton hope, the midfielder scoring with a stunning, first-time, right-foot volley from a dozen yards, connecting with a right-wing cross from Tony Hibbert.
But United's next attack capped their golden spell and appeared to have settled any lingering doubt about the game's outcome.
Former Everton favourite Rooney and Welbeck exploited the growing gaps at the back of the Everton defence, exchanging passes which allowed the England striker to race clear and bury the ball emphatically past Howard.
With the score at 4-2, United's Patrice Evra hit the post with a header.
Everton though were clearly in the mood to have a decisive say in the title race. After 82 minutes, Phil Neville's pass forward saw Fellaini rise with two defenders, the ball breaking kindly for Jelavic who converted clinically from eight yards.
United were rattled and there was an air of inevitability about the equaliser, two minutes later. Neville again set up the goal with his pass finding Fellaini who turned brilliantly before laying the ball off for the unmarked South Africa star Pienaar to score, on the run, from the six-yard line.
The frantic activity merely raised the stakes on what had been an equally absorbing first period in which the title race seemed to have taken a dramatic twist after 33 minutes when Everton capped what had been an impressive start to the game by taking the lead through Jelavic, the forward signed in the January transfer window by David Moyes.
Former United midfielder Darron Gibson started the move with a pass wide to the right wing and overlapping full-back Hibbert whose deep cross hung in the air invitingly, allowing Jelavic to out-jump Rafael and send a perfect header looping back across David de Gea into the United goal.
Five minutes before the interval, United were level aas Evra fed Nani wide on the left and the winger made space before curling over an expert cross which Rooney planted into the Everton goal via a bouncing header.
It was the 180th goal of Rooney's United career, good enough to lift him into fourth place on the club's all-time scoring charts, but not enough, on this occasion, to bring his team three much-needed points.
In the last minute of the five added on at game's end, Rio Ferdinand drew an excellent save from Howard, who tipped his shot over the bar.