A last-gasp goal from Domic Calvert-Lewin denied Manchester United the win they wanted to mark the 63rd anniversary of the Munich tragedy and draw level on points with neighbours City at the top of the Premier League table.Calvert-Lewin pounced from close range in added time to earn Everton a draw just as United thought the three points were in the bag.
Goals from Edinson Cavani and Bruno Fernandes gave United a 2-0 lead at the break but Everton had wiped that out within seven minutes of the second period starting with goals from Abdoulaye Doucoure and James Rodriguez.
Scott McTominay restored United’s lead with a header from Luke Shaw’s free-kick but Calvert-Lewin pounced to level it at the death. 
United have now conceded 18 goals in 12 Premier League home games this season, one more than they did in the whole of last season at Old Trafford.
The hosts will be wondering how they conspired to throw away victory here, especially having gone into half-time two goals up thanks to Cavani’s fine header and Fernandes’ moment of magic.
Everton were level within seven minutes of the second half getting under way as Doucoure turned home before Rodriguez rifled home the leveller, only for McTominay to head home Luke Shaw’s free-kick.
The hosts, buoyed by the win against Saints, started the brighter, with Mason Greenwood whipping in a superb left-footed cross that Mason Holgate put behind after it just evaded Cavani.
ED IT IN SON: Man Utd’s Edinson Cavani celebrates scoring his side’s opener at Old Trafford
Paul Pogba’s header from the resulting corner was hacked clear and Greenwood was soon causing problems again, turning Andre Gomes inside out before hitting a mishit shot across the face of goal.
The France international, who was named United’s Player of the Month for January, pulled up with what looked to be an issue with his right thigh, leading Fred to replace him in the 39th minute.
Victor Lindelof was breathing a sigh of relief after his clearance under pressure was blocked and Richarlison subsequently sent an effort across out-of-position De Gea’s goal, before Fred missed as the first half looked set to peter out.
But Fernandes had other ideas. Without options on the edge of the box, he struck a sublime right-footed shot that beat Olsen and nestled in the top left-hand corner.
But while Everton may have ended the first half with their shoulders slumped, they had their tails up after the break.
Shortly after a Shaw snapshot was denied by Olsen, Calvert-Lewin was sent through and De Gea could only parry his shot into the path of Doucoure.
That 49th minute blow was soon followed by another gut punch. United’s defence failed to effectively clear a cross and Doucoure drove a ball back to Rodriguez, who took a touch and fired a low left-footed strike past De Gea.
Solskjaer’s side were rocked on their heels but slowly began to regain their composure and build pressure, with Rashford forcing Olsen into a save at his near post.
United edged back ahead in the 70th minute. Shaw sent in a fizzing free-kick from the left and McTominay directed it past Olsen.
Fernandes and Rashford tried to extend United’s lead and avoid a nervy ending, with Lucas Digne hitting the foot of the post before Richarlison fired off target at the other end.
They were warning shots that United failed to heed. Deep in stoppage time, Digne’s free-kick was flicked on by Keane and Calvert-Lewin pounced from close range.
MAN UTD: De Gea 5, Wan-Bissaka 6, Lindelof 5, Maguire 5, Shaw 7; McTominay 7, Pogba 5 (Fred 38, 6); Greenwood 6, Fernandes 8, Rashford 7; Cavani 7.
Subs not used: Martial, James, Henderson, Alex Telles, Matic, Williams, van de Beek. 
EVERTON: Olsen 5; Holgate 6, Keane 6, Godfrey 6, Digne 6; Doucoure 6 (King 81, 5), Gomes 5 (Iwobi 75, 5), Davies 5; James 6 (Sigurdsson 69, 5), Richarlison 6, Calvert-Lewin 7.
Subs not used: Delph, Mina, Nkounkou, Bernard, Coleman, Virginia.
Referee: Jonathan Moss.