Gabriel Jesus made Arsenal's win safe with almost the last kick
In a chaotic finale to a largely scrappy game, United first thought they had snatched three points only to see Alejandro Garnacho's 88th-minute finish ruled out for offside by the video assistant referee with the score 1-1.
The drama then switched to the other end in eight added minutes as Declan Rice's deflected shot gave Arsenal the lead before substitute Gabriel Jesus raced clear to wrap up the win as the stadium exploded in elation.
United had taken the lead in the 27th minute when Christian Eriksen's outstanding pass played in Marcus Rashford, who cut inside to send an unerring right-foot drive past Arsenal keeper Aaron Ramsdale.
The Gunners, who had already spurned a golden chance when the struggling Kai Havertz miskicked with the goal at his mercy, were level almost instantly when captain Martin Odegaard was given too much space and sent an emphatic finish into the bottom corner.
In an encounter that rarely hit the heights despite lots of effort, Arsenal - who had seen a penalty over-turned by the VAR after referee Anthony Taylor originally ruled Havertz had been fouled - missed a glorious late opportunity when Bukayo Saka shot straight at Andre Onana.
United saw celebrations cut short with two minutes left when substitute Garnacho raced clear to score, but the VAR ruled he was just offside - opening the door for Arsenal to produce two devastating blows.
-- Courtesy of BBC Sport