Jose Mourinho's side had won the last four league matches against its fierce North West rival but was forced to settle for a solitary point in a tense encounter that failed to live up to the huge pre-match hype.
No team can better Liverpool's 73 Premier League goals since the arrival of Jurgen Klopp last October, but its swashbuckling attack was kept firmly in check by a United defence superbly screened by Ander Herrera and Marouane Fellaini.
Chances were almost non-existent in the first half, but Zlatan Ibrahimovic spurned the best opening of the first hour when he contrived to head Paul Pogba's curling cross away from the Liverpool goal.
David de Gea saved superbly to deny Emre Can as Liverpool continued to do most of the attacking work, with the introduction of fit-again Adam Lallana from the bench adding renewed impetus to its approach, and the Spain number one clawed a thunderous Philippe Coutinho strike away from the top corner 10 minutes later.
Substitute Wayne Rooney entered the fray for the final 13 minutes but the out-of-favour United captain could not repeat his winner in the same fixture last season, as a packed Anfield - in which there seemed to be no repeat of the unsavoury chanting about which both clubs had warned their fans - was forced to settle for a stalemate.
United enjoyed the better of a tense opening 15 minutes, though Ibrahimovic and Pogba blazed well over the crossbar with their first two meaningful efforts on goal.
Loris Karius reacted well to push a devilish Marcus Rashford cross away from the path of Ibrahimovic, before Roberto Firmino spurned a decent chance for Liverpool by heading straight at De Gea just before the half-hour mark.
Liverpool regained a degree of composure and enjoyed the majority of possession late in the half, but United's disciplined rearguard restricted the host to two shots on goal - its joint-lowest tally in the first half of a home league game since 2003-2004.
Karius almost gifted United the lead just after the break when he passed straight to Pogba 18 yards out, but the assistant referee's flag rescued the 23 year-old just as Ibrahimovic aimed to pounce.
But the former Sweden captain had nobody to blame after 54 minutes when he headed Pogba's fine deep delivery across the six-yard box and to safety with the goal seemingly at his mercy.
Liverpool at last found a way through the United defence when Joel Matip played in Can, but De Gea sprung low to his right to deny the Germany international after he struck a low shot towards the bottom corner.
Coutinho was denied a stunning winner from 30 yards when De Gea leapt to his left to palm the Brazilian's dipping shot past the post - a save that even drew applause from Klopp on the touchline - but there was to be no late winner at either end.
The result takes Liverpool to within two points of league leader Manchester City, while United is three further back in seventh place.