The striker has now scored seven goals in as many games since Gabriel Jesus suffered his knee injury.
Marcus Rashford netted in superb fashion to give United a 1-0 lead but this goal was cancelled out by Nketiah before Bukayo Saka’s top-drawer finish had Arsenal in front.
Lisandro Martinez, an Arsenal target last summer, then levelled for United following some poor defending but Nketiah would turn home a wayward Martin Odegaard shot to secure a memorable win.
Having seen an eight-point lead at the summit cut to just two following back-to-back victories for Manchester City since Arsenal’s win at Tottenham, Mikel Arteta’s side delivered when the pressure was on.
United are the only side to beat the Gunners in the Premier League this season and made a good start in their bid to repeat September’s Old Trafford win.
They had an early penalty shout turned down as Bruno Fernandes was challenged by Aaron Ramsdale, the VAR’s swift check backing up referee Anthony Taylor’s call to wave away appeals, but were nevertheless celebrating the lead in the 17th minute.Thomas Partey uncharacteristically lost possession cheaply before Rashford skipped past him and arrowed in a fine low finish.
Arsenal, showing the sort of response of any side with title ambitions, bounced back soon after as Nketiah nodded home a Granit Xhaka cross after losing Aaron Wan-Bissaka far too easily.
The game opened up from that point, Scott McTominay – in for the suspended Casemiro – forced a smart stop out of Ramsdale with a strike from the edge of the box.
Arteta was booked by referee Taylor following his protestations at a Luke Shaw foul on Saka as the first half ended with the sides locked level.
That would change just eight minutes after the restart as Saka, afforded too much space and time, curled home an inch-perfect strike from 25 yards to put Arsenal ahead.
Ramsdale put in a man-of-the-match display in the 2-0 win at Spurs last week and made a great save to deny Rashford levelling with a deflected effort.
The England goalkeeper, however, was culpable for United’s equaliser after a mix up with half-time substitute Takehiro Tomiyasu at a corner allowed Martinez to head in his first Red Devils goal.
Having shared four goals, both teams went in search of the winner as Saka struck from a similar position only for this effort to deflect off Christian Eriksen and clip the post.
Leandro Trossard, who joined Arsenal from Brighton on Friday, came on for the final 10 minutes to make his Arsenal debut as David de Gea made a smart close-range stop to deny Nketiah a second.
Arsenal were now very much on top with United unable to get out of their own penalty box for large spells.
Eriksen led a rare foray forward for the visitors, winning a corner for a brief respite but the Arsenal pressure eventually told as Nketiah’s reaction to throw a boot at an Odegaard effort saw him divert the ball past De Gea.
A VAR check followed but the former England Under-21 striker was played onside by Wan-Bissaka and the goal was awarded, sending the Emirates wild and putting Arsenal five points clear of City with a game in hand.