Jurgen Klopp’s side came into the game level on points with champions City, who were not in Premier League action this weekend due to facing Chelsea in the League Cup final.
However, the title contenders looked some way below their best, as they made basic errors and struggled to find any sort of fluidity.
United were hindered by a series of first-half injuries as Ander Herrera, Juan Mata and Jesse Lingard all came off, the latter having already been brought on as a substitute.
Liverpool also suffered a crucial injury of their own as they lost Roberto Firmino in the opening 45 minutes.
In the second half, United had the ball in the net from a Joel Matip own goal, but it was ruled out for Chris Smalling being offside.
Smalling had another opportunity to take all three points for the hosts in the final minutes of the match too, but failed to make contact with a good ball from Romelu Lukaku.