A 70th minute strike from Georginio Wijnaldum proved to be enough for Liverpool on a difficult afternoon in Sheffield.
It was an ugly win, but a win regardless that sends the Reds 8 points clear at the Premier League summit ahead of the rest of the weekends' fixtures.
Story of the match
United set up as expected. They defended deep, denying Liverpool space and forced them into wide areas.
Despite conceding possession in the early stages, it was in fact the hosts who had the first chance of the game.
The Reds were caught out on the counter and Oliver McBurnie had a go with his right foot, shooting straight at Adrian.
Jurgen Klopp's side were tasked with breaking down a well-drilled, resilient and compact Sheffield defence and patience would be key on Saturday afternoon at Bramall Lane.
Joel Matip constructed Liverpool's first real chance of the game, threading a fantastic ball through to forward players.
Nothing came of it and Wijnaldum's eventual shot was deflected out for a corner.
The European Champions' first shot on goal came on the 16 minute mark, which is the longest they've waited since April.
As the first-half drew to a close, the visitors' put together a few good chances, causing the Blades' back line some real problems for the first time.
An inch-perfect ball from Virgil Van Dijk found the run of Sadio Mane and the number 10 was able to stay onside.
Mane scuffed his shot and it flew wide, concern was growing that Liverpool weren't at their clinical best and this could've turned into a real problem as United were defending so brilliantly.
On the brink of half-time, Liverpool found themselves with a rare counter-attacking opportunity and some good build up saw the front three work the ball into the box.
Roberto Firmino placed the ball on a plate for Mane who tried to sneak it in at the near post, but it rebounded off and Firmino was unable to get a shot away.
Liverpool needed to be better second-half and some positive play saw Matip drive through the midfield and find Jordan Henderson out wide.
The captain put a teasing ball into the box but it just evaded Mane and Firmino, and it was collected comfortably by the Sheffield keeper.
As the clock ticked towards 70 minutes and after substitutions were made, the hosts had the opportunity to go ahead.
Liverpool were forced into some last-ditch defending, Andy Robertson had to run in and make a fantastic block following some fantastic footwork from John Fleck.
The midfielder turned Fabinho by cutting inside but his effort was cut off by the left back.
Just moments later, Liverpool found their breakthrough with a volley from Wijnaldum.
The Dutch International was in space on the edge of the box and volleyed the ball towards the Blades keeper, Henderson should've saved it but it went between his legs and creeped over the line.
But, he more than made up for his calamitous error when Mohamed Salah picked up a loose ball and was 1v1 with Henderson but he was quick to get down and deny the Egyptian.
He may have cost them earlier in the second-half, but he most definitely kept them in the game in that moment as it looked a certain goal for Salah.
Sheffield could've and probably should've equalised on 85 minutes as Leon Clarke was played in through the Liverpool defence, the striker then blazed it over the bar.
Replays showed he looked a fraction offside, but it was a tight call and a massive let off for the Reds.
Takeaways from the match
Liverpool able to grind out results
Liverpool fans saw it in the back end of last season and will be pleased to see it carry on into this campaign.
They won't always be at their free-flowing, clinical best but league-winning sides are able to win games regardless.
Chris Wilder's side are definitely the most resilient defensive set-up the Reds have faced so far, and they had to be patient in order to break them down.
Is the VAR intervention bar too high?
The "clear and obvious error" approach has caused yet more controversy today as Liverpool were denied another penalty.
A late challenge on Mane in the box was waved on by referee Anthony Taylor and VAR didn't intervene, despite no contact with the ball being made.
This leads into the debate that the "clear and obvious" bar could be too high and that VAR should be stepping in to assist with more decisions.
Problems continue down Liverpool's right hand side
It's no secret that opposition teams target Trent Alexander-Arnold when looking to get forward.
With Van Dijk and Robertson defending the opposite flank, it's understandable - but teams are causing Liverpool problems.
The young full-back can be left isolated at times, giving opposition players some joy.
Stand-out players
Van Dijk once again looked brilliant for Liverpool. A calm and assured presence at the back, the Dutch defender keeps the Reds in games at times.
He's there for last-ditch defending when necessary but his pass towards Mane before half-time, creating the 1v1 shows what he can provide going forward as well.
The entire Sheffield defence deserve enormous credit for their showing today.
They restricted the space, cut off passing lanes and kept the front three quiet - something most teams struggle to do.
Liverpool got themselves over the line today and proved they're capable of winning difficult games in different ways.
This is a fixture that would've ended as a draw or defeat in previous seasons, but Klopp's 'mentality monsters' are able to find a way to win, even if it's an ugly win.
They're next in action on Wednesday night as they look to put points on the board in their UEFA Champions League group when they face RB Salzburg at Anfield.
Sheffield United travel to Watford next weekend in search of a second consecutive away League win.