Scott McTominay's first-half strike put United in front at a wet Old Trafford on Monday but Arsenal struck back 13 minutes into the second period through the prolific Pierre-Emerick Aubameyang.
A low-quality match saw few chances to snatch all three points thereafter, McTominay having the best opportunity to win the game but failing to convert a United corner while Marcus Rashford's free-kick was saved by Bernd Leno in added time.
In driving Manchester rain it took until the 29th minute - the longest wait in the league this season - for the game's first shot, Leno saving easily from Andreas Pereira's low drive.
The match slowly opened up with Nicolas Pepe testing David de Gea at his near post, the goalkeeper then making a fine double save to deny Bukayo Saka and Matteo Guendouzi.
United struck moments before half-time, McTominay lashing home a stunning 20-yard strike for his first Old Trafford goal after Daniel James and Marcus Rashford led a rapid break.
Arsenal hit back in the 58th minute as VAR correctly overruled a terrible offside decision from the linesman after Axel Tuanzebe gave the ball away in a bad position.
Bukayo Saka seized on Tuanzebe's loose pass and fed Aubameyang, who stole through to beat De Gea with a clever chipped finish for his seventh Premier League goal of the season.
Paul Pogba bent a shot just wide as United tried to respond then McTominay should have restored their lead from an Ashley Young corner, planting a free header well over the crossbar.
United looked likelier to win it late on but Leno brilliantly saved from Rashford before De Gea had to deny substitute Reiss Nelson at the death.
What does it mean? Champions League return a long way away
The fact this game was being played on a Monday, 24 hours before Manchester City and Tottenham will be in Champions League action, will not have been lost on fans of United and Arsenal. On this display, returning to Europe's elite any time soon is improbable for both teams, although the draw leaves Arsenal in fourth with United three points back in 10th place.
Saka a star in the making
Alexandre Lacazette's ankle injury has provided a chance for Saka to shine and the 18-year-old is taking it with both hands.
He has been directly involved in four goals in his four appearances in all competitions this season and earned praise from Cesc Fabregas on Twitter, the former Arsenal star writing: "Saka is a player. 18 years old showing great maturity."
Saka is a player. 18 years old showing great maturity— Cesc Fàbregas Soler (@cesc4official) September 30, 2019
Xhaka ducking feeds the narrative
McTominay's rocket looked destined for the top corner as soon as it left his right boot, but Arsenal's new official club captain Granit Xhaka arguably could have blocked it. Replays appeared to show Xhaka ducked his head away from the ball's flight instead of getting in the way.
It is tempting to speculate whether Patrick Vieira or Tony Adams, two Gunners greats who wore the armband in more successful times for Arsenal, would have risked a bloody nose and stopped the shot.
Key Opta Facts
- Manchester United's haul of nine points after seven games this season is their worst tally at this stage of a top-flight season since 1989-90 (7 points).
- Arsenal are unbeaten in consecutive Premier League games at Old Trafford (D2) for the first time since January 2000.
- Manchester United have won 49 points from their 28 Premier League games under Ole Gunnar Solskjaer – two fewer than they won in their final 28 games under Jose Mourinho.
- McTominay's goal was his first for Manchester United at Old Trafford, in his 25th home game for the club in all competitions.
- Aubameyang is the first Arsenal player to score as many as seven goals in their first seven Premier League games of a season since Dennis Bergkamp in 1997-98.
- Aubameyang has scored 14 goals in his last 14 starts in the Premier League for Arsenal.
Both teams are in Europa League action on Thursday, with Arsenal hosting Standard Liege while United are away to Eredivisie outfit AZ. In the Premier League at the weekend it is Newcastle United away for the Red Devils and Arsenal are at home to Bournemouth.