A remarkable second half at Old Trafford - featuring a repertoire of brilliant goals - concluded with United throwing away a 4-2 lead as Nikica Jelavic and then Steven Pienaar silenced Old Trafford by drawing Everton level.
At half time it was only 1-1 following goals from Wayne Rooney and Jelavic during a rather tentative first 45 minutes from United, but the game exploded in the second period as Old Trafford was treated to six further goals, the first two of which came in three minutes from Danny Welbeck and Nani as United turned on the style.
Marouane Fellaini's fine volley looked to be nothing but a consolation when Rooney restored United's two-goal lead with his 180th goal for United, taking him clear of George Best and Dennis Violett in fourth place in United's all-time list, but a dramatic conclusion to proceedings saw United reined in by a spirited Everton as their defence crumbled.
The result means United are now only three points clear of Manchester City at the top of the table following their rivals' victory at Wolves later on Sunday, and if Roberto Mancini's side win their remaining three games of the season - including the Manchester derby at home on April 30th - then they will be named Premier League champions.
United's solitary change from the 4-0 win over Aston Villa last weekend was to replace Ashley Young with Nani, a high profile decision given Sir Alex Ferguson admitted this week he had had words with the England international after Young was subjected to sustained criticism for two dives in recent games.
Everton, meanwhile, were missing highly influential left-back Leighton Baines due to a hamstring injury, but Pienaar returned to the starting XI having been ineligible for last weekend's FA Cup semi-final defeat at the hands of Liverpool.
Nani was United's main threat in the opening exchanges - going close with two smart shots from the left side of the box - but Everton started the better side and created the first clear-cut opportunity after five minutes when Leon Osman played in Jelavic with a clever little pass and the Croatian striker forced David De Gea into action with a firm drive.
United were guilty of a somewhat lethargic performance in Sunday's early kick-off, while by contrast Everton were a model of application, eschewing a negative approach to take the game to the hosts and break regularly with intent, with Fellaini a combative influence in the centre of midfield.
Another midfielder - Darron Gibson, returning to the club he departed in January - shot wide from range before United were then left exposed in the air to go 1-0 down after 33 minutes. Tony Hibbert swung in a deep, deep cross from the right and Jelavic was free at the back post to cushion a perfect header back over De Gea from the tightest of angles.
The goal appeared to shake United out of their stupor and the league leaders almost mustered an immediate response when the ball popped out to Paul Scholes following a corner and his shot took two deflections before being stopped by a fine reaction save from Howard.
On 41 minutes they did carve out an equaliser. Michael Carrick poked a pass out to Patrice Evra under pressure and the Frenchman slipped the ball quickly to Nani. He cut back onto his right foot before producing a glorious cross to find Rooney, the striker getting in behind Phil Neville to convert with a header from close range.
Rooney had only previously scored twice in 11 league games against his former club, but after netting for the sixth home league game in succession he drew level with the great Best and Violett on 179 career goals for United.
Strike partner Welbeck had looked bright in patches during the first half but after the break he came to exert a much bigger influence on the game, putting United in front after 57 minutes with a brilliant finish.
Though Everton were angered by referee Mike Jones's refusal to stop play for an injury to Pienaar having done so when Evans was down in an incident in the first half, United played on and when the ball bounced into the path of Welbeck on the edge of the box he made space with a neat dummy before caressing the ball into the top corner.
Welbeck's strike instigated a frantic, end-to-end period in which four goals were scored in the space of 12 minutes. Nani was the next to get on the scoresheet on the hour mark: United constructed a lovely passing move that culminated with Welbeck releasing the winger with a lovely little reverse pass and Nani produced an equally delightful finish when dinking the ball over the advancing Howard.
Where Nani favoured finesse, Fellaini's reply after 67 minutes relied on a potent combination of technique and power as he met a cross from Hibbert, again, with a well-executed volley that flew past De Gea and into the bottom corner.
Pienaar then called De Gea into action with a firm drive but just as the game threatened to spiral out of control for United, Rooney restored a modicum of calm with his second of the afternoon. Welbeck was central to proceedings again as he first spun away following a lovely dummy to collect Rooney's pass, and then squared for his team-mate to tap the ball in past Howard as Old Trafford was treated to another goal of the highest quality.
United appeared destined for a 13th win in 15 Premier League games but remarkably Everton's enterprise was rewarded with two late goals, and only after Evra had spurned the chance to put the game beyond doubt when striking the post with a header.
On 83 minutes, the presence of Fellaini caused havoc in the United box and the ball bounced to the unmarked Jelavic, who continued his impressive form since joining the club in January when sweeping the ball home from adjacent to the penalty spot.
Still Everton were not finished, and on 85 minutes they were level when United found themselves cut open once again. Neville played the ball into Fellaini and the big Belgian spun in the box before playing a beautiful square pass for Pienaar, who slotted the ball to the side of De Gea to make it 4-4.
With the title swinging the way of City, United piled forward for a winner in injury time and almost had it when Rio Ferdinand saw a thunderous effort tipped over the bar by Howard. However, Everton held on for the most remarkable of points, and a result that may yet see United deposed as champions of England.