Manchester United keeper David de Gea produced a world-class save to deny Joel Matip as Liverpool were frustrated by Jose Mourinho's stubborn side at Anfield for the second successive season.
Jurgen Klopp's side peppered the United goal with 19 shots but a combination of outstanding goalkeeping by Spain keeper De Gea and the home team's poor finishing denied them a decisive moment.
The German's men were in control of the game for long periods but their profligacy in front of goal means they have now won just once in eight games.
The most noteworthy incident of an uneventful first half was De Gea denying Cameroon defender Matip from close range with a brilliant reflex save with his outstretched left boot, before Mohamed Salah fired the rebound wide.
United offered very little quality in attack although De Gea's counterpart Simon Mignolet had to smartly parry Romelu Lukaku's fierce attempt before the interval.
Liverpool dominated even more after half-time but Emre Can wasted their best chance when he volleyed over the bar from eight yards after being picked out by the impressive Joe Gomez.
The point leaves United - with nine clean sheets in their past 10 league games - two points behind Manchester City, who thrashed Stoke 7-2.