The Gunners remain on course for a first title in 19 years with a game in hand over City also to come.
United went in front at the Emirates after Marcus Rashford’s thunderous strike opened the scoring with his ninth goal since the World Cup break.
Arsenal levelled within seven minutes as Nketiah’s powerful header rounded off a brilliant team move.
Bukayo Saka’s long-range effort that arrowed into the bottom corner put the home side in front early in the second half.
This time United bounced straight back when Lisandro Martinez, who had been a target for Arsenal before arriving at Old Trafford in July, headed in a loose ball from a corner.
Erik ten Hag’s men were penned inside their own box for much of the final quarter as the post denied Saka a second and David de Gea saved from Nketiah.
Arsenal’s pressure finally got its reward when Nketiah flicked home Martin Odegaard’s shot and the goal survived a VAR check for offside.
“Emotional, a lot of passion, a lot of quality. It doesn’t get much better than that,” said Arteta.
“To come here against this team and play the way we played. The second half especially, the performance was incredible.”
A first defeat in 11 games realistically ends any hope of United’s first title in a decade as they slip 11 points behind Arsenal in fourth, having played a game more.
“It’s hard to accept when you lose in the last stage of the game,” said Ten Hag.
“We made mistakes with all three goals. Normally we are better in such situations. It can’t happen.”
Haaland’s fourth hat-trick
Haaland’s fourth hat-trick in 19 Premier League appearances had briefly cut Arsenal’s lead at the top to two points as Pep Guardiola got the reaction he wanted from the defending champions.
Guardiola questioned his players’ hunger to retain the title after Thursday’s 4-2 win over Tottenham.
Haaland is the one major difference to Guardiola’s previous title-winning sides in England and the Norwegian silenced any doubts over whether City are a stronger force without a recognised striker.
The 22-year-old’s scoring rate has slowed marginally in recent weeks, but his header from Kevin De Bruyne’s cross moved him level with the 23 league goals that saw Mohamed Salah and Son Heung-min share the Golden Boot with last season.
Haaland then took his tally to 30 goals in all competitions from the penalty spot early in the second half after Ilkay Gundogan had been upended by Ruben Neves.
Wolves gifted Haaland his hat-trick four minutes later as goalkeeper Jose Sa presented the ball to Riyad Mahrez, who unselfishly squared for his teammate to roll into an unguarded net.
“The numbers are incredible,” said Guardiola.
“We can’t play the false nine with him. You have to adapt some movements with him and we are doing quite well.”
Just a second league defeat since Julen Lopetegui took charge leaves Wolves above the relegation zone only on goal difference.
Leeds edged one point clear of the bottom three, but remain without a league win since November after a 0-0 draw at home to Brentford.