Marcus Rashford's 17th goal of the season fired Erik ten Hag's side into an early lead in North London, before Eddie Nketiah's header levelled matters just eight minutes later.
The ever-threatening Bukayo Saka then scored to put the Gunners ahead with just eight minutes played of the second half, curling an effort beyond the on-reaching David De Gea.
Lisandro Martinez's smart looping header evaded the best attempts of William Saliba, drawing the Reds level going into the final half an hour.
But it was to be heartbreak late on, as Nketiah's second of the afternoon handed Mikel Arteta's side all three points in an end-to-end encounter.