In a game of few chances, the Reds were indebted to goalkeeper David de Gea, who kept out Joel Matip with a world-class reflex save in the first half to preserve United's unbeaten league record.
United will be much the happier with a hard-earned point and could even have completed the ultimate smash-and-grab.
Romelu Lukaku, isolated and on the periphery throughout, fired straight at Simon Mignolet when well-placed.
Georginio Wijnaldum went close from distance early on, and Nemanja Matic - impressive again - then did likewise at the other end with a 30-yarder.
Clear cut chances proved hard to come by, but Liverpool should have taken the lead ten minutes shy of the interval.
Roberto Firmino's cut-back found Matip, but his snapshot from six yards out was brilliantly turned away by de Gea's outstretched foot when the centre-back seemed certain to score. Liv
After Phil Jones had partially cleared, Salah then should have done better with the rebound but pulled his angled effort narrowly wide.
At the other end, Lukaku spurned a glorious opening in front of the Kop.
Neat one-touch play on the edge of the area between Henrikh Mkhitaryan and Anthony Martial released the Belgian, but his shot lacked power and compatriot Mignolet parried away the effort.
Liverpool almost caught United napping soon after the interval, with de Gea to the rescue once again.
Philippe Coutinho picked out Firmino, Jones blocked the initial shot before the Spanish stopper blocked bravely at the feet of the forward as the hosts ratcheted up the pressure.
Emre Can volleyed over from ten yards when one-on-one, and Firmino was then flagged offside having burst clear.
Jurgen Klopp's side continued to press, but United held firm and then introduced Jesse Lingard and Marcus Rashford - who was carrying a knock - in an attempt to snatch an unlikely win.
For once, Jose's substitutions did not have the desired effect, however, and the breakthrough remained elusive as United held out.
City won 7-2 against Stoke later on Saturday to move two clear, but this was a point gained as attentions turn to the midweek Champions League trip to Portugal.
Overall team performance: 6/10
United Faithful Man of the Match: David de Gea