Jurgen Klopp's Liverpool would have drawn level on points with leaders Manchester City with a fifth successive Premier League victory, but were subdued by a classic Jose Mourinho performance of defensive organisation and discipline.
United did not allow Liverpool to build the momentum and intensity that has characterised their game this season, while Mourinho's limited attacking ambitions ensured chances were at a premium.
The Portuguese was still grateful for two fine second-half saves from goalkeeper David de Gea, who dived low to stop Emre Can and saved athletically from Philippe Coutinho's 25-yard effort.
United's best chance also came in the second half, but the unmarked Zlatan Ibrahimovic directed Paul Pogba's cross off target.
The visitors had just 35% of possession - their lowest in a Premier League match since Opta began recording the data in 2003-04.
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While this deadlock does little for the ambitions of both teams, there is no doubt who will be the happier manager.
This was, in so many respects, the most Mourinho performance of his short time at United.
Klopp came on to the pitch at the final whistle to applaud Liverpool's fans, but there was a tinge of disappointment in his measured tread as he trudged off.
His side's promising start to the season has been built on pressing opponents into submission - a high-pressure style that has brought victories at Arsenal and Chelsea, as well as nine goals in two home wins against Leicester City and Hull City.
But Mourinho picked a powerful, athletic side and instructed them to turn the tables on Liverpool's pressing game.
Ander Herrera was at the heart of United's smothering gameplan, almost operating in the pockets of Coutinho and Roberto Firmino in midfield, while Liverpool were never given a second.
They simply could not find a way through.
United held their shape and discipline, much to their manager's satisfaction, although he still needed those two superb saves from De Gea, and a magnificent saving tackle from Antonio Valencia to stop Firmino as he raced in on goal.
It was classic Mourinho, a tactic he has perfected and utilised throughout his career, and Anfield's increasing anger and frustration will have been music to his ears.
This match should have been the perfect stage for the £89m Pogba - but once again he was a peripheral figure.
The world's most expensive player was used in a more advanced role and is certainly on the same wavelength as Ibrahimovic, delivering a perfect cross which the Swede should have converted.
In other aspects, though, he operated on the margins of the game and failed to exert the influence expected of a player of his quality and experience.
United will expect much more as the season goes on.
Anthony Taylor was the man in the middle in every sense after the heat generated by the appointment of the Manchester-based official for a meeting between these two fierce rivals.
Mourinho said the appointment made it "difficult" for Taylor, and put him under pressure - comments being investigated by the Football Association - while former referee Keith Hackett even suggested it represented a risk to his and his family's safety.
It certainly increased the scrutiny on Taylor, who felt the wrath of The Kop within minutes - complete with colourful reminders about his place of residence - when he did not book Marcus Rashford for a foul on James Milner.
It was to the official's credit that he did not buckle in the atmosphere, kept discipline without resorting to a rash of yellow cards, and controlled a game that always has explosive potential.
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Liverpool manager Jurgen Klopp: "I am not frustrated but I am not happy with the performance. No-one will show this game in 10 or 20 years but we could have played better.
"It was a hectic game, interrupted here and there, but we lost patience with our passing game. The attitude of my team was really good. We were ready to fight but when you can play better, you have to.
"The kind of defence is difficult to play. The man-marking is really difficult, they are stronger than us. We wasted energy in the first half for nothing. The second half was better and with fresher legs in second half we could have created more."
Manchester United boss Jose Mourinho: "It is not the result we wanted but it is a positive result. It is a result that stops a direct opponent getting three points at home, so not a bad result.
"The game was difficult for both teams but for longer periods it was more difficult for them than us.
"We controlled the game not just tactically but the emotion of the game. That was probably the quietest Anfield I had and I was expecting it to be the other way.
"It was a positive performance."
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Former Wales midfielder Robbie Savage on BBC Radio 5 live: "Liverpool have not played well tonight and United have done a job.
"It is the first points that Liverpool have dropped at Anfield. Mourinho has done his job.
"He got a point so it was the right thing to do. They lost a few games this season and have come to Liverpool and got a draw, so you have to say job done.
"But in an attacking sense they offered nothing."
United are next in action when they host Fenerbahce in the Europa League on Thursday (20:05 BST) before returning to Premier League action at Mourinho's former club Chelsea on Sunday (16:00 BST).
Liverpool host West Brom in the 17:30 BST Premier League match on Saturday.
Match ends, Liverpool 0, Manchester United 0.
Second Half ends, Liverpool 0, Manchester United 0.
Substitution, Manchester United. Luke Shaw replaces Ashley Young.
Marouane Fellaini (Manchester United) is shown the yellow card for a bad foul.
Adam Lallana (Liverpool) wins a free kick in the defensive half.
Foul by Marouane Fellaini (Manchester United).
Foul by Jordan Henderson (Liverpool).
Paul Pogba (Manchester United) wins a free kick in the defensive half.
Zlatan Ibrahimovic (Manchester United) is shown the yellow card for a bad foul.
Emre Can (Liverpool) wins a free kick in the defensive half.
Foul by Zlatan Ibrahimovic (Manchester United).
Dejan Lovren (Liverpool) wins a free kick in the defensive half.
Foul by Zlatan Ibrahimovic (Manchester United).
Substitution, Liverpool. Alberto Moreno replaces James Milner.
Substitution, Liverpool. Divock Origi replaces Roberto Firmino.
Attempt blocked. Nathaniel Clyne (Liverpool) right footed shot from the right side of the box is blocked. Assisted by James Milner with a cross.
Sadio Mané (Liverpool) wins a free kick in the attacking half.
Foul by Paul Pogba (Manchester United).
Attempt missed. Marouane Fellaini (Manchester United) header from the centre of the box is close, but misses to the right. Assisted by Daley Blind with a cross following a corner.
Corner,  Manchester United. Conceded by Emre Can.
Attempt missed. Emre Can (Liverpool) right footed shot from outside the box is close, but misses to the right.
Attempt blocked. Nathaniel Clyne (Liverpool) right footed shot from outside the box is blocked. Assisted by Philippe Coutinho.
Substitution, Manchester United. Wayne Rooney replaces Marcus Rashford.
Offside, Manchester United. Marouane Fellaini tries a through ball, but Zlatan Ibrahimovic is caught offside.
Offside, Liverpool. Adam Lallana tries a through ball, but Roberto Firmino is caught offside.
Attempt blocked. Philippe Coutinho (Liverpool) right footed shot from the left side of the box is blocked.
Delay over. They are ready to continue.
Delay in match James Milner (Liverpool) because of an injury.
Delay in match Marcus Rashford (Manchester United) because of an injury.
Foul by Joel Matip (Liverpool).
Chris Smalling (Manchester United) wins a free kick in the defensive half.
Corner,  Liverpool. Conceded by David de Gea.
Attempt saved. Philippe Coutinho (Liverpool) right footed shot from outside the box is saved in the top right corner. Assisted by Emre Can.
Foul by Emre Can (Liverpool).
Antonio Valencia (Manchester United) wins a free kick in the defensive half.
Sadio Mané (Liverpool) wins a free kick in the defensive half.
Foul by Daley Blind (Manchester United).
Foul by Roberto Firmino (Liverpool).
Chris Smalling (Manchester United) wins a free kick in the defensive half.
Corner,  Liverpool. Conceded by Chris Smalling.
Liverpool and Manchester United played out a goalless and uneventful stalemate on a disappointing night at Anfield.