Mason Greenwood came off the bench to rescue a point for Manchester United as Everton's improvement under Duncan Ferguson continued in a 1-1 draw.
Everton played with great tenacity and character, taking the lead courtesy of a Victor Lindelof own-goal (37) but United always carried a threat and substitute Greenwood skilfully drilled one home from the edge of the box to level it home (77).
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With injuries mounting up, this was a big point gained for Everton and stand-in boss Ferguson, who has now taken four points from his two games in charge against 'big-six' teams.
Ferguson also showed a ruthless side to his management style, replacing Moise Kean on 88 minutes after bringing him on as a substitute 18 minutes earlier. The Italian striker, who wasn't injured, headed straight down the tunnel.
For United, it brings them back down to Earth as they never came close to hitting the heights of their sensational 2-1 win at Manchester City last weekend.
Man Utd: De Gea (5), Wan-Bissaka (7), Lindelof (5), Maguire (6), Shaw (6), McTominay (5), Fred (7), James (6), Lingard (5), Rashford (6), Martial (5)
Subs: Greenwood (8)
Everton: Pickford (5), Coleman (7), Keane (7), Holgate (8), Mina (7), Digne (N/A), Davies (6), Iwobi (6) , Bernard (5), Calvert-Lewin (9), Richarlison (8)
Subs: Baines (7), Kean (N/A), Niasse (N/A)
Man of the match: Dominic Calvert-Lewin
How Ferguson revolution thwarted United…
United had won 36 of their 54 Premier League games against Everton (drawing nine and losing nine), more than any side has won against another in the history of the competition - and they started full of tenacity and confidence.
United were unchanged from their win over Manchester City but Djibril Sidibe (illness), Theo Walcott (calf), Morgan Schneiderlin (illness) and Gylfi Sigurdsson (calf) were all missing for Everton so Seamus Coleman, Yerry Mina, Tom Davies and Bernard entered the fold.
Jesse Lingard curled a shot just wide inside 15 seconds as Everton would've been forgiven for thinking a long afternoon lay in wait.
However, United didn't really build on their bright beginning with only Marcus Rashford and Daniel James threatening with strikes from tight angles that Jordan Pickford watched wide.
Everton grew into the half with Richarlison and Dominic Calvert-Lewin providing a platform for them to build. That pressure paid off on when they took the lead on 36 minutes.
Leighton Baines, on as a substitute for the injured Lucas Digne, whipped in a typically ferocious delivery from a corner which caused problems for David de Gea, who was under pressure from Calvert-Lewin. The goalkeeper could only feebly flap the ball straight at Lindelof who didn't react in time to stop the ball from rolling into the net. VAR checked for a possible foul on De Gea by Calvert-Lewin but saw no reason to overturn the decision.
United continued to snatch at chances in the second half with Pickford not suitably tested until Luke Shaw stung his gloves on 62 minutes.
Ole Gunnar Solskjaer sent on Greenwood three minutes later after the youngster had impressed in midweek with two goals against AZ Alkmaar. It was a decision that yielded maximum rewards as Greenwood levelled the game when United were struggling for inspiration.
The 18-year-old found half-a-yard of space on the edge of the area and drilled an arrow-like strike into the bottom corner leaving a fully-stretched Pickford with no chance.
Ferguson remained positive with his substitutions despite losing the lead but controversially hooked Kean for Oumar Niasse having brought the Italian on just 18 minutes earlier. Ferguson ignored the player as he walked past him on the touchline and headed straight for the dressing room.
Everton didn't have many scares in the closing stages as Ferguson surely has thrown his hat firmly in the ring for the permanent job.
Man of the match: Dominic Calvert-Lewin
Outstanding. As Sky Sports co-commentator Gary Neville put it, Calvert-Lewin's display was straight out of the Duncan Ferguson handbook as the young Everton forward fought, harassed and bullied his way to a performance of prominence despite Everton's scarcity of possession.
The best player on the pitch by a country mile.
What the managers said...
Manchester United boss Ole Gunnar Solskjaer said: "We're disappointed that we didn't get three [points]. Towards the end we ran out of time and we didn't have the ideas to win it.
"But we put pressure on them, kept them on the back foot and there was never any doubt that if there was one team who was going to win it I felt it was us.
"They are always dangerous on counter-attacks and set plays so you're never sure but we came back after a disappointing half-time at 1-0 down.
"You shouldn't concede goals like this, set plays again but we'll work on them."
Everton boss Duncan Ferguson said: "It was tremendous. What a fantastic performance the boys put in, what a shift, unbelievable, we just couldn't hang on there.
"We tried to change the shape a little bit but just couldn't get the information on but they were fantastic to a man.
"At the moment I'm delighted because we've got a point, of course we were winning but I can't complain.
"United came on strong in the second half but we looked good on the counter-attack as well and had one or two chances when Dominic [Calvert-Lewin] broke forward, if we could have just found that final pass... But I thought the boys were absolutely immense."
- Manchester United have lost just one of their last 27 home league games against Everton (W20 D6 L1).
- Everton have won only one of their last 12 away Premier League games (D4 L7), taking just seven points from a possible 36.
- Manchester United are without a clean sheet in their last 12 league matches - their worst run since a 12-game stretch between April and August 1971.
- Only Rashford (13) has more goals in all competitions for United this season than 18-year-old Greenwood (7).
- Greenwood was the youngest scorer (18y 75d) at Old Trafford for Manchester United in the Premier League since Federico Macheda in April 2009 against Aston Villa (17y 226d).
United host Colchester in a Carabao Cup quarter-final on Wednesday before travelling to Watford next Sunday, a game live on Super Sunday. Meanwhile, Everton host Leicester in their quarter-final on Wednesday ahead of a home clash with Arsenal in the Premier League on Saturday.