First-half injuries to United trio Ander Herrera, Juan Mata and Jesse Lingard and Liverpool forward Roberto Firmino put paid to hopes of a classic between English football's two most successful clubs.
The best chance of the game fell to Lingard before he succumbed to injury in the first half, but Alisson Becker was more than a match, stretching out an arm as the midfielder tried to round him.
Liverpool were far from their fluid best but had a measure of control throughout, securing a point that lifts them above champions Manchester City. United drop to fifth, a point outside the top four as Arsenal beat Southampton 2-0 in the day's other Premier League game.
United were nervous in the opening exchanges of a half Liverpool controlled. With just 20 seconds on the clock, Ashley Young's under-hit backpass was handled by David de Gea before Firmino could pounce. Mata blocked James Milner's indirect free-kick but Liverpool settled sooner.
United lost Herrera to a hamstring and Mata to hip injury inside 25 minutes, with Andreas Pereira and Lingard stepping into a makeshift midfield line-up - which already included Scott McTominay as Nemanja Matic missed out through injury - that struggled to contain an encouraged Liverpool side.
Players continued to drop like flies, with Firmino rolling his ankle and Lingard forced off before the interval, but only after the half's best chance had fallen the way of the England international.
Paul Pogba found Romelu Lukaku on the edge of the area and his disguised through-pass released Lingard through on goal where he tried to round Alisson, but the Liverpool goalkeeper's outstretched arm nicked the ball off his toes.
It was Lingard's last involvement before he succumbed to a recurrence of a hamstring injury, the substitute being substituted as the introduction of Alexis Sanchez left Solskjaer with no options from the bench for the second half.
A battling second-half display from United ensued and, cheered on by their passionate home crowd, they nearly secured a victory that would have dented Liverpool's title hopes.
United had the ball in the back of the net on 75 minutes when Joel Matip turned into his own net from a Chris Smalling cross, but the United defender was correctly ruled offside.
Smalling could not stretch far enough to apply the finishing touch to a Lukaku cross in the final minute, but there was to be no winner as both sides settled for a point.
Player ratings
Man Utd: De Gea (6), Young (6), Smalling (7), Lindelof (7), Shaw (8), Herrera (5), McTominay (7), Pogba (8), Mata (5), Rashford (7), Lukaku (6).
Subs: Pereira (7), Lingard (5), Sanchez (6).
Liverpool: Alisson (7), Milner (6), Van Dijk (7), Matip (6), Robertson (6), Fabinho (6), Henderson (6), Wijnaldum (6), Firmino (5), Mane (6), Salah (5).
Subs: Sturridge (5), Shaqiri (n/a), Origi (n/a).
Man of the Match: Luke Shaw.
The managers
OLE GUNNAR SOLSKJAER;
Everything that could have gone wrong in the first half went wrong — Ole
Ole Gunnar Solskjaer admits he was concerned about Marcus Rashford's injury during the 0-0 draw with Liverpool, but was forced to leave him on because of other injury problems.
Ole Gunnar Solskjaer: "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. But I can't remember Liverpool having a chance. Even though they had possession, I can't remember David de Gea making a save.
KLOPP:
UNITED SHOULD HAVE BEEN BEATEN - KLOPP
Jurgen Klopp admits his side struggled to find their rhythm in the 0-0 draw with Manchester United, but he was happy with his players' attitude
Klopp believes Liverpool should have taken advantage of Manchester United's injury crisis in Sunday's stalemate at Old Trafford.
Liverpool returned to the top of the Premier League with a point from the goalless draw, but it could have been much more after United lost Ander Herrera, Juan Mata and Jesse Lingard to injury before half-time.
"In this game, on days when United are beatable you have to do it and we didn't do it," Klopp admitted in his post-match interview
"It was intense, that was clear, but in the situation today that's a point won for United and we lost two."
Liverpool controlled possession in the first half but uncharacteristically created very little in attacking areas, with the best chances falling to United.
Klopp attributed Liverpool's toothless display to a loss of rhythm caused from the multiple first-half injury stoppages, which also included the loss of Roberto Firmino.
"It was strange game," he added. "We started really well, we started exactly how we wanted to start.
"Then the injury crisis started, and it obviously cost us the rhythm. It happened to us with Bobby and that was a catastrophe.
"We lost the rhythm and couldn't get it back. We played, they had set pieces, not really counter-attacks, it was a game without a lot of highlights I would say.
"At the end United played with a completely new midfield, a completely new three up front."
Opta stats
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.
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 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).
Jesse 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.
Manchester 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).
PUNDIT SPEAKS
Jamie Carragher says Liverpool's front three 'haven't quite exploded' yet this season and says they will need to step up if they are to win the league
SEE OTHER RESULTS
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