It was the third game in the last five between the clubs at Anfield that has ended goalless and will have left many frustrated but United will be happy to remain top of the league and with a three-point advantage over their North West rivals.
United are the first time to stop Liverpool scoring at Anfield in the Premier League since October 2018 but that was as much to do with the champions' lack of creativity and sharpness in the final third as United's solid defending.
Alisson saved a close-range effort from Bruno Fernandes, United's first real chance, in the 75th minute with his feet to deny the Portuguese midfielder.
Then Alisson did well to keep out a blast from inside the box by Paul Pogba who was picked out by Aaron Wan-Bissaka in the inside-right slot and lashed a snap-shot goalwards which the Liverpool keeper showed great reflexes to deal with.
Ole Gunnar Solskjaer's United side finished what was a disappointing game the stronger but the Norwegian felt his team could have taken all three points.
"It was an opportunity missed with the chances we had but then again we were playing a very good side. I'm disappointed but still a point is OK if you win the next one," he said.
The result leaves United on 37 points, two ahead of second-placed Leicester City, while Juergen Klopp's Liverpool side are third on 34 points after 18 games.
It was the third successive game in which Liverpool's usually prolific strikeforce failed to score and Klopp will be concerned that his team created few openings for the forwards.
Injuries meant Liverpool had to play midfielders Fabinho and Jordan Henderson in central defence and they coped well, keeping Rashford and Anthony Martial quiet for long periods.
"With all the things said before the game - they're flying and we're struggling - my boys did a good game," said Klopp.
"First half the counter-press was great, passing was good. But we didn't score. That's the most important thing in football," added the German.
Liverpool stretched their unbeaten home record to 68 games while United remain unbeaten away this season.