Jesse Lingard was on the pitch for just 17 minutes but had the best chance of the game when he was denied by Alisson.
Liverpool got the point they needed to return to the top of the Premier League but were left frustrated by their failure to break down a Manchester United side that was ravaged by injuries.
A draw at the home of their fiercest rivals would usually be seen as mission accomplished for Jurgen Klopp's side, but this has to go down as something of a wasted opportunity to get some daylight over nearest rivals Manchester City.
Injuries to three midfielders meant United were forced to use all of their substitutes in a bizarre 25-minute period before half-time with one of them, Jesse Lingard, quickly being replaced himself.
Liverpool did not escape unscathed, with Roberto Firmino only lasting until the half-hour mark, and without him his side struggled to pose any sort of threat in front of goal in what was was a typically intense encounter.
The constant disruptions made for a disjointed first half and neither side could truly find their rhythm after the break - although the lack of quality did not affect the raucous atmosphere throughout.
Klopp's side failed to truly test United keeper David de Gea, with a shot from distance by Firmino's replacement Daniel Sturridge their only shot on target in the 90 minutes.
United had the best chance of the game, but Alisson brilliantly denied Lingard after he ran on to Romelu Lukaku's pass and attempted to go around the Reds keeper.
The hosts thought they had stolen victory near the end when Liverpool defender Joel Matip put through his own net from a free-kick, but Chris Smalling was adjudged offside in the build-up.
With Manchester City in action in the Carabao Cup final on Sunday, the result means Liverpool move a point ahead of them with 11 games to go.
United drop to fifth place, with Arsenal leap-frogging them with their win over Southampton.
Injuries spoil Solkjaer's plansManchester United midfielder Jesse Lingard replaced Juan Mata as a substitute but had to go off before half-time with a hamstring injury.
United do not factor in this season's title race but this was still an important game for interim boss Ole Gunnar Solskjaer's ambitions to become their manager on a permanent basis.
This was his chance to show that the tactical nous that has brought him success on the road at Tottenham, Arsenal and Chelsea could bring him his biggest result so far at Old Trafford.
Sadly for Solskjaer, those plans were scuppered by injuries, much as they were in United's Champions League defeat here by Paris St-Germain when he lost Anthony Martial and Lingard by the midway point of the game.
This time he was without Nemanja Matic from the start, with the Serbian injured in training on Saturday morning.
Matic's replacement, Scott McTominay, was making his first league start since Solskjaer took charge in December and ended up being one of the outstanding players of United's makeshift midfield.
First Ander Herrera was forced off, to be replaced by Andreas Pereira after 21 minutes, with Juan Mata limping off four minutes later after he was hurt in a crucial challenge with Mohamed Salah.
Mata was replaced by Lingard, returning to action for the first time since that PSG defeat, and he looked set to make a decisive impact before being denied by the brilliance of Alisson, who got down smartly to nick the ball off his feet.
Instead, Lingard appeared to tweak a hamstring as he stumbled beyond Alisson and was himself replaced by Alexis Sanchez before half-time.
Understandably, those changes left United lacking spark in attack - especially because Marcus Rashford played on despite also appearing to pick up an injury early on.
At the other end, however, United yielded nothing, and Solskjaer deserves nothing but credit for the way he reorganised his side.
Liverpool's attack a concern for KloppLiverpool forward Mohamed Salah only had one shot before he was replaced in the 79th minute by Jurgen Klopp
Liverpool's travelling fans were kept in their seats until long after the final whistle and used their time to noisily and repeatedly salute their side's return to the summit.
This was a result the majority would surely have accepted before kick-off, but the manner they earned their draw as they used up their game in hand over City was far from convincing.
There was a spell in the first half when Liverpool were winning the ball back in dangerous areas and putting pressure on United but, even then, their lack of cutting edge was apparent.
When Firmino was on on the pitch, Salah and Sadio Mane struggled to impose themselves on the home side's defence and, when the Brazilian departed, the rest of Liverpool's front-line all but disappeared too.
With United sitting back in the second half, Liverpool had much more of the ball but, just as they did against Bayern Munich on Tuesday, Klopp's side struggled to do very much with it.
Their inability to open up opposition teams when they defend in numbers must be a concern for Klopp, because they are sure to meet more sides who will do the same in the next few weeks.
400th day at the top - the best of the statsManchester United's David De Gea kept his 100th clean sheet in the Premier League; the seventh goalkeeper to do so for a single club and the second for Man Utd after Peter Schmeichel (112).
This draw has taken Liverpool top of the Premier League, meaning today will be the 400th day they have finished top of the table in the competition's history.Liverpool have played out back-to-back goalless draws in all competitions for the first time since April 2013 (v West Ham and Reading) under manager Brendan Rodgers.Manchester United have failed to score in back-to-back games at Old Trafford in all competitions for the first time since December 2015 against PSV Eindhoven and West Ham United with Louis van Gaal in charge.Liverpool have managed to win just two of their last 18 visits to Old Trafford in all competitions (D3 L13), and only one of their last 13 (D3 L9).Lingard became the first player to be substituted on and then off in the first half of a Premier League match since Kevin Long for Burnley against Newcastle United in January 2015.Manchester United were the first team to make all three substitutions in the first half of a Premier League game since Burnley in January 2015 vs Newcastle United.There were four substitutions made in the first half of this match - the most in a single Premier League game since Wigan v Fulham in February 2009 (also four).This was the fifth draw played out by Manchester United and Liverpool in their last seven meetings in all competitions (one win each), as many as their previous 50 encounters combined beforehand.'We didn't do well' - KloppEverything went wrong in the first half - Solskjaer
Manchester United manager Ole Gunnar Solskjaer, speaking to BBC MOTD: "Everything that could have gone wrong in the first half went wrong. We had four injuries - we had to keep Marcus Rashford on - it seemed like it was going to be a tough afternoon.
"I can't remember Liverpool having a chance. Even though they had possession, I can't remember David de Gea making a save. Scott McTominay was excellent. When they need a goal and they take Mohamed Salah off you know Luke Shaw has played a good game."
Liverpool didn't create enough - Klopp
Liverpool manager Jurgen Klopp, speaking to BBC Match of the Day: "We might feel like we won a point or lost two. We started exactly how we wanted to start. The injury crisis then started.
"We were without chances - only United had one big one when Alisson made an excellent save - the rest were set-pieces. It kept the game open but we didn't create enough and that's the truth. We didn't do well to be honest. We take that. It is a point gained because we have one more than before but it doesn't feel like that.
"The boys didn't feel okay. I could see it in their faces. It was strange. I was thinking 'what is gong on here today'. They lost momentum and rhythm and couldn't really get it back."
Man of the match - Scott McTominay (Manchester United)Before Sunday he had played only 17 minutes of league football under Solskjaer and almost left the club on loan in January. He returned to the starting XI to put in the kind of performance of discipline and steel that United’s depleted midfield badly needed to help keep Liverpool quiet.What next?
Liverpool are back at Anfield on Wednesday when they play Watford (20:00 GMT) then travel across Stanley Park to face neighbours Everton on Sunday (16:15 GMT). Manchester United travel to Crystal Palace on Wednesday (20:00), then host Southampton on Saturday (15:00).