In an action packed match, United forward Marcus Rashford put his side ahead with a powerful shot from 25 yards out that left goalkeeper Aaron Ramsdale stunned, however, their lead only lasted for six minutes before Nketiah headed Arsenal back level from Granit Xhaka‘s cross.
The second half saw more goals as a winger Bukayo Saka drove in from the left wing hitting a sensational finish low into the far corner past the outstretched United goalkeeper David de Gea in the 53rd minute.
This time it was United who responded six minutes later, with a defender Lisandro Martinez taking advantage of a fumble from Ramsdale and diving for a header to make it two a piece.
In the dying minutes of the game, Nketiah found himself on the end of a pass from Martin Odegaard and calmly finished into the bottom right corner to give the home side the win and prove why Arsenal are at the top this season.
Arsenal remain top of the table, five points ahead of Manchester City with a game in hand, while United are in third 11 points off the leaders.