Jadon Sancho opened the scoring for Man United in the 50 minutes during the encounter.
However, Chelsea levelled through Jorginho’s penalty 19 minutes later.
The result means Chelsea are still on top of the Premier League table with a point ahead of second-place Manchester City.
Man United, on the other hand, are in 8th position with 18 points from 13 games.
Chelsea’s next fixture is against Watford on December 1, while Man United will play Arsenal on December 2.