Man United vs Everton post match, Match reaction & Highlights 2021, Man United 3 Everton 3 Goals Ole Gunnar Solskjaer's post match,
But Scott McTominay's header put United back in front - until the late, late drama saw it finish 3-3.
Everton were abysmal in the first half, and found themselves 2-0 down at the break.
Edinson Cavani's header and Bruno Fernandes' brilliant 25-yard chipped effort had Ole Gunnar Solskjaer's side firmly in control.
But the visitors incredibly had the game level at 2-2 just seven minutes into the second half thanks to strikes from Abdoulaye Doucoure and James Rodriguez.
In-form McTominay restored the home side's lead with a superb header on 70 minutes.
But Calvert-Lewin was the Toffees hero as he bravely stabbed the ball home in second half injury-time.
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Manchester United 3-3 Everton: Dominic Calvert-Lewin grabs LAST-MINUTE equaliser in six-goal thriller as Ole Gunnar Solskjaer's men miss out on the
chance to move level on points with City despite leading twice at Old Trafford
Manchester United: De Gea, Wan-Bissaka, Lindelof, Maguire, Shaw, Pogba (Fred 39), McTominay, Greenwood (Tuanzebe 90), Fernandes, Rashford, Cavani
Subs not used: Henderson, Telles, Williams, James, Matic, Van de Beek, Martial
Goals: Cavani 24, Fernandes 45, McTominay 70
Booked: Shaw, Tuanzebe
Manager: Ole Gunnar Solskjaer
Everton: Olsen, Holgate, Keane, Godfrey, Digne, Doucoure (King 81), Davies (Iwobi 75), Gomes, Richarlison, Rodriguez (Sigurdsson 69), Calvert-Lewin
Subs not used: Delph, Mina, Nkounkou, Bernard, Coleman, Virginia
Goals: Doucoure 49, Rodriguez 52, Calvert-Lewin 90+5
Manager: Carlo Ancelotti
Edinson Cavani edged United in front with a bullet header at the back post from Marcus Rashford's delivery
The hosts doubled their lead just before half-time when Bruno Fernandes smashed in a strike from distance
Abdoulaye Doucoure and James Rodriguez hauled Everton level soon after the break to stun the home team
Paul Pogba was forced off with an apparent thigh injury in a blow for United and the in-form French midfielder
Scott McTominay flicked home a header from Luke Shaw's free-kick to restore United's lead on 70 minutes
But Dominic Calvert-Lewin later broke free to divert home a last-gasp finish and rescue a late point for Everton