Liverpool controlled the game at Anfield for large periods but both teams did not do enough on Merseyside as a meeting between these two clubs ended in a draw for the fourth successive game.
The result sees United edge ahead of Manchester City in the table after a seventh clean sheet in eight league matches, while Liverpool have now won just one of their last eight fixtures in all competitions.
The opening stages of the showdown between the two North-West giants were fiercely contested, but chances were few and far between with only a scuffed effort from Georginio Wijnaldum coming close to a goal.
United looked threatening on the break - especially through Ashley Young who was being used further forward - but the opportunities continued to be created by Liverpool, with Joel Matip firing over the crossbar and Wijnaldum curling straight at David de Gea.
During the opening quarter of the game, Romelu Lukaku touched the ball just once and it highlighted the amount of possession that Liverpool were having, but most of it was coming in non-threatening areas.
On the half-hour mark, Nemanja Matic drilled a volley marginally wide of Simon Mignolet's post, but the chance of the first half fell to Matip, who was denied from eight yards by a stunning block from De Gea before Mohamed Salah sent the rebound wide.
Liverpool were building momentum as the half-time whistle approached but just before the break, United should have scored through Lukaku, who fired too close to Mignolet from 14 yards out after being teed up by Anthony Martial.
After the restart, Philippe Coutinho was moved into a more central area and the switch had its desired effect with the Brazilian soon beginning to pull the strings for Liverpool.
However, the first clear-cut opportunity of the second half fell to Emre Can after the midfielder was found by a teasing cross from Joe Gomez, but the German international somehow flicked the ball over from no more than eight yards.
Jose Mourinho did not wait to make changes to his misfiring side, with Henrikh Mkhitaryan and Martial being withdrawn with more than a quarter of the match still to go, but United remained on the backfoot as Liverpool tried to find a decisive goal.
Jurgen Klopp's men were dominating possession, but openings were not being created and after waiting until 11 minutes to go, the German finally made changes with Alex Oxlade-Chamberlain and Daniel Sturridge being introduced into the action.
Neither man was able to contribute anything to Liverpool's cause, however, with only a tame header from Dejan Lovren coming anywhere near to breaking the deadlock in the closing stages.
It reached a point where United were prepared to run down the clock in order to confirm a result which extends their unbeaten record in all competitions to 11 games, while Liverpool were forced to be content with yet another draw in front of their own supporters.