Although the winning goal came late, the result was fair.
It was Arsenal who had the most and best chances and pressed.
There was a big hug party on the field and the fans stayed for a long time and sang.
Arsenal now have a five-point lead over Manchester City with a game less played at the top of the table.
With six minutes of normal time remaining, the ball bounced in United's penalty area and Eddie Nketiah pulled hard from a couple of yards, a shot that David De Gea reflexively saved.
Nketiah had taken aim.
In the last regular minute, Nketiah made it 3-2 after twisting the ball in near the goal.
The incident was video reviewed from several conceivable offside situations.
The cheers were deafening at the Emirates when the goal was conceded.
Shot from long range by Saka made it 2-1
Arsenal trailed tlll 2-1 at the start of the second half.
Bukayo Saka had the ball far from goal and pulled a hard shot.
David De Gea was on his way into the goal and didn't have time to get back to the far side of the cage where the ball went in.
A couple of minutes later, the Argentinian Lisandro Martinez (new world champion) equalized to make it 2-2 after a corner.
Arsenal goalkeeper Aaron Ramsdale didn't get a good hit on the ball when he cleared it.
Martinez, wearing a black headband, lunged forward and headed the ball into an arc, where Gabriel tried to head it away unsuccessfully.
With 20 minutes to go, Saka got into a new position from the right wing and fired a sizzling shot that hit the outside of the post as he sought out the same corner again.