In a pulsating game at the Emirates, both sides traded the lead before Lisandro Martinez's equaliser in the second half for United appeared to send the clash towards a draw. But Nketiah, who cancelled out Marcus Rashford's opener with a first-half header, claimed victory for Arsenal in the final minute to keep the Gunners five points clear of Manchester City at the top of the table.
Here are some quick thoughts about Sunday's standout Premier League fixture.
1. Arsenal pass another huge test in their title charge
January was supposed to be the acid test of Arsenal's surprise challenge for the Premier League title, but Mikel Arteta's team keep on proving the doubters wrong with big results, and none will be more significant than this 3-2 win against Manchester United.
The Gunners were held by Newcastle at the start of the month, but won at Tottenham last week before avenging their only defeat of the season so far against United. And in beating United, Arsenal displayed the qualities of champions. They fought back from conceding an early goal, went on to take the lead and then scored a late winner after the visitors had made it 2-2 midway through the second half.
Arsenal have yet to play champions Manchester City this season, so the clash against a resurgent United was the biggest test of Arteta's team. And they answered all the questions asked of them to beat Erik ten Hag's side.
Arsenal are now at the halfway stage of the season and have amassed 50 points from 19 games. Even if they drop off from that incredible pace in the second half of the season, they will still finish the campaign with a huge points total; the pressure is on City to reel them in, but this Arsenal side is playing without fear and nerves.
Both may come, of course, but right now they are showing the same kind of carefree form that propelled Leicester to the title in 2016. And unless City can beat them in their first league meeting next month, it will become increasingly difficult to see how anyone can stop Arsenal from winning the title.
2. Weghorst makes a difference, but United still lack attacking edge
Wout Weghorst is not the answer to Manchester United's goal-scoring problems, but he is certainly giving Erik ten Hag's team something different up front. The Netherlands international, on loan from Burnley until the end of the season, has been brought in to bolster United's attacking options following Cristiano Ronaldo's mutually-agreed departure in November.
With Anthony Martial still sidelined with a hamstring injury, the 6-foot-6 Weghorst started his second successive game at the Emirates and, just as on his debut at Crystal Palace, he didn't threaten the opposition goal. But Weghorst has made United more direct and given them the option to hit the ball long when needed. It would be wrong to suggest that he is merely a target man, though.
Weghorst is good with his feet and he linked played well with his attacking teammates and also drew players to mark him whenever the ball was in the air, freeing space for the likes of Marcus Rashford and Antony. He also has a much greater work ethic than Martial and is prepared to endlessly press the opposition defence. But ultimately, he is limited in his ability to beat his marker and opponents know that they can keep Weghorst at bay fairly easily.
United have the lowest goal tally in the top six and right now, they're being rescued by Rashford's goals time and time again. That won't continue forever, so they need to be more potent. Weghorst gives them another option, but he won't score enough goals to make United serious title contenders.
3. Arsenal have a right-back problem
Mikel Arteta has worked wonders to turn Arsenal into title challengers, but his team still has flaws, and nowhere more than at right-back.
Ben White was awful in the first half and completely failed to make life difficult for Rashford. He was also outdone more than once by Bruno Fernandes as United repeatedly attacked down their left-hand side.
The former Brighton defender is primarily a centre-half, but he has operated at right-back throughout this season because Gabriel and William Saliba have been so impressive in the middle of the Arsenal defence. White is simply not equipped to play at right-back. He thinks like a centre-back and it means he often makes the wrong decisions.
Arteta substituted White at half-time -- it may have been an injury, but there was no indication of that -- and replaced him with Takehiro Tomiyasu, but the Japan defender was no better than his teammate and arguably even worse.
Obviously, being asked to defend against Rashford in this kind of form is tough for any player, but there are other great wide players in the Premier League and Arsenal will face them during the battle for the title.
To avoid their clear weakness being targeted, Arteta needs to find a solution -- and fast.
Best and worst performers
Eddie Nketiah, FW, Arsenal: He's proving to be much more than merely a stand-in for the injured Gabriel Jesus. Great goal to equalise in the first-half and was in the right place at the right time to score the winner.
Lisandro Martinez, DF, Man United: Rejected a move to Arsenal to sign for United last summer and Erik ten Hag will be delighted with the Argentina defender's performances. This was one of his best, with a goal too.
Bukayo Saka, FW, Arsenal: Scored an outstanding goal and then hit the post when trying to do the same again. United had no answer to the Arsenal winger.
Ben White, DF, Arsenal: The Arsenal right-back was turned inside and out by Rashford and lacked conviction in too many challenges. A real weak-link in the Gunners' team.
Aaron Wan-Bissaka, DF, Man United: Lost Nketiah at the far post for Arsenal's equaliser and unreliable when he had possession. Like White with Arsenal, Wan Bissaka just wasn't up to the job.
Antony, FW, Man United: Another game without any kind of positive impact by United's £85 million summer signing. All left foot and not quick enough to go past his defender ... what does he actually do?
Highlights and notable moments
Rashford's sparkling form must be noted, especially as he opened the scoring on Sunday with a brilliant, thundering effort from distance to beat Aaron Ramsdale.
However, after a brilliant back-and-forth game, up stepped Nketiah with the decisive moment in the 90th minute.
After the match: What the players/managers said
"It was a great game with a lot of tempo and the audience is the big winner. Two top teams, but of course we are disappointed when you lose this game at a late stage. All the goals we conceded today are mistakes: it can't happen. Even last week, we were so hard to beat in such situations. Today we were not. All three goals, we could have avoided.
"They are very good on the ball, but we are a good defending team. There were not a lot of open chances. We made mistakes which we cannot make. This game was decided by small details but also the decision making. That is hard to accept and we have to learn from it... I want to win. It is not good enough. We want to be the number one but not if we make mistakes. That is clear and what I told them." -- Manchester United boss Erik ten Hag speaking to BBC Sport
"Emotional, a lot of passion. It doesn't get much better than that. The second half especially, the performance was incredible. We were composed and determined at the same time. We never panicked. We always believed that we could win it. We showed the right composure in the box a lot of times but the ball didn't go in. Thankfully at the end it did.
"It's great and we deserve where we are because of how we're playing. But there are a lot of things that we can do much better." -- Arsenal manager Mikel Arteta, speaking to Sky Sports
Key stats (provided by ESPN Stats & Information research)
Arsenal: Restores 5-point lead over Manchester City in Premier League standings; 63% chance to win Premier League per FiveThirtyEight's Soccer Power Index
Arsenal: 50 points through 19 PL games are the 5th most by a club at this stage of a Premier League season
Arsenal: Extends PL unbeaten streak to 13 games (11-0-2 W-L-D), its longest Premier League unbeaten run since 14, from Aug.-Dec. 2018
Eddie Nketiah: Seven goals in last seven appearances in all competitions after scoring two goals in his first 18 games this season
Marcus Rashford: Nine goals in nine games in all competitions since the post-WC restart; that is more than he scored in 19 games pre-World Cup (8) for Manchester United this season; Rashford's 9 post-restart goals in all competitions are the most among players in Europe's top 5 leagues
Bukayo Saka: Scored in 3 straight Premier League games vs. Man United, joins Arsenal legends Freddie Ljungberg (1998-2000) & Thierry Henry (2000-01) as the only Arsenal players to score in 3 straight PL apps vs Man United.
Arsenal: It doesn't get any easier for the Gunners after Sunday's hard-fought win. First they face a trip to Manchester City on Friday for an FA Cup fourth-round clash, followed by struggling Everton away on Feb. 4 in the Premier League.
Manchester United: Thanks to United's progress in the Carabao Cup, they face a busy fortnight of games in several competitions. After a Wednesday visit to Nottingham Forest (Carabao Cup semifinal, first leg), they host Reading (FA Cup, fourth round) on Jan. 28 before the return leg of their semifinal with Forest on Feb. 1. From there, just a couple of days' rest before their next league clash, a home game vs. Crystal Palace, on Feb. 4. It's exhausting to type, let alone play in.