Following their ridiculous 4-3 loss to Chelsea midweek, United boss Erik ten Hag said pre-match that his players would be positive and be in the mood to turn things around.
With this in mind, his players almost got off to an electric start and netted within two minutes after Bruno Fernandes played Alejanrdo Garnacho through on goal and the Argentine forward rounded Caoimhin Kelleher and fired home - but the celebrations were cut short as it was ruled out for offside.
From that moment on, Liverpool were firmly on top, producing shot after shot on André Onana’s goal. First, Dominik Szoboszlai saw an effort saved by the United goalkeeper, but Onana’s resolve was broken midway through the half.
Andrew Robertson’s corner was nodded to the back post by Darwin Núñez, where Luis Díaz, completely unmarked, was able to net with a scissor kick.
The Reds continued to dominate for the rest of the half, but both Mohammed Salah and Núñez failed to double the visitors’ lead with their multiple efforts.
Jürgen Klopp would have been pleased to go into the break with the lead, but perhaps disappointed with it only being 1-0 having had 14 shots to United’s zero - the first time the Red Devils had failed to produce a shot in the first half at Old Trafford since October 2015.
United came flying out for the second half as a completely different outfit and equalised in the 50th minute thanks to a moment of brilliance from captain Bruno Fernandes.
Jarrell Quansah played a square-ball near the halfway line but out of his eyeline was Fernandes lurking, and the Portuguese maestro produced a sublime first-time effort from just inside the Liverpool half that nestled in the corner.
Klopp’s men responded well after the scores were levelled, but United completed unlikeliest of turnarounds in the 67th minute. Aaron Wan-Bissaka picked up the ball on the left flank and picked out Kobbie Mainoo in the box, allowing the midfielder to turn and curl a spectacular pinpoint effort into the far corner.
Klopp was visibly enraged at his defence, who themselves were having their own postmortem as to how the visitors were now a goal down.
Liverpool came back once again with waves of attacks however and Harvey Elliott won a penalty for the Reds in the last 10 minutes after being brought down by Wan-Bissaka.
Salah stepped up and slotted the resulting penalty kick away to draw level and set up a grandstand finish.
Wave after wave of Liverpool attack followed, with Díaz squandering their best chance on the half-volley from close range, as United's makeshift defence held firm to ensure spoils were shared between the two old rivals.
Flashscore Man of the Match: Luis Díaz (Liverpool)