City earlier beat bottom club Sheffield United 1-0 to move to 44 points from 20 matches while United are on 41 points from one game more.
Third-placed Leicester City, who are on 39 points, will go above Manchester United if they can beat Leeds United on Monday.
Following their shock home defeat by Sheffield United on Wednesday, United boss Ole Gunnar Solskjaer reverted to his strongest side although he lost Scott McTominay during the first half.
Arsenal were without the injured Bukayo Saka and Kieran Tierney and had key striker Pierre-Emerick Aubameyang missing due to COVID protocols.
United's best opening in the first 45 minutes fell to Marcus Rashford but the England forward over-elaborated and the opportunity passed.
After a disappointing first half, Arsenal came out strongly following the interval and Willian had a good chance in the 49th minute which was well blocked by Aaron Wan-Bissaka.
Harry Maguire also produced a fine block to deny Nicolas Pepe as the Gunners piled on the pressure and Alexandre Lacazette came closest to scoring with a 56th-minute curling free kick that struck the bar.
Emile Smith Rowe then forced a good save out of United keeper David De Gea with a low drive but Mikel Arteta's side slowly ran out of ideas.
United created little with their two chances after the break falling to Edinson Cavani who sent a low Luke Shaw ball wide and, in the final minute of normal time, he attempted a difficult volley from a Wan-Bissaka cross which flashed past the post.
United set a new club record of 18 away games unbeaten in the league while Arsenal, eighth on 31 points, have not lost since in seven matches since Christmas.
United's Shaw was not happy with a draw that means his side had dropped five points since last week's FA Cup win over Liverpool.
"Two points dropped I feel. The chances we had, I don't think it's acceptable to come away with a point...I'm sure the lads will be disappointed," he said.
"At times we were too slow. Second half we were sloppy and gave the ball away. We created the chances and failed to score again and it cost us two points.
"If we want to be in the title race we have to be winning these games," he added.
Arsenal's Brazilian defender David Luiz said the team were continuing to progress.
"You have to be humble because we are far from the first positions. We have to think game by game and at the end of the season we will see how far we can go," he said.
"The ambition is to be fighting for the first positions - that ambition has to be there."