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Jurgen Klopp’s side were by far the better team against Sheffield United but had to sweat for its 3-1 victory, with a top-class strike from the Argentinian with 14 minutes to go giving them control.

The World Cup-winner has become a hugely-influential player in the last few weeks playing in a more advanced position – although he started this game as the holding midfielder before moving forward – and his goal had echoes of Steven Gerrard against Olympiacos in 2005.

Whether it proves to be as significant as the one which paved the way for their Champions League win will only be discovered over the next eight games but in the short term it took Liverpool two points clear of Arsenal and three ahead of Manchester City.

With games running out every victory leaves even less margin for error for their rivals, which was why Mac Allister’s goal, an unstoppable strike into the top corner from the edge of the penalty area, was so important after the chasers had both won on Wednesday.

Darwin Nunez’s 18th of the season – courtesy of a mistake from goalkeeper Ivo Grbic – had given the host a 17th-minute lead, only for Conor Bradley’s own goal just after half-time to ratchet up the tension.

The classy Mac Allister, one of the most composed players on the pitch, relieved that and substitute Cody Gakpo’s late effort was an added boost to the goal difference which could yet be crucial.

United have conceded 80 goals this season – more than any other top-flight team, with 14 of those coming in the last four outings.

Their first half was indicative of why they are bottom of the league and destined for a swift return to the Championship as a failure to take gilt-edged chances and an inability to avoid mistakes proved costly.

Sunday’s visitors Brighton scored after 90 seconds but the Blades could have even beaten that when former Liverpool academy graduate Jack Robinson’s long throw was flicked on to James James McAtee at the far post but he shot straight at Caoimhin Kelleher from just a few yards.

Ben Brereton-Diaz then flicked the resulting corner wide and while taking either of those chances may not have been enough for the leakiest side in the top flight it would have at least given them something to cling on to.

Instead they shot themselves in the foot as, after Mohamed Salah had a chip tipped over by Grbic, the United goalkeeper was culpable for the opening goal.

The Croatian dithered too long in clearing a backpass and that was all the invitation Nunez needed to charge him down, with the clearance rebounding off him into an unguarded net.

Mac Allister, Dominik Szoboszlai and Luis Diaz all had attempts, while Ryan Gravenberch showed his lack of recent game time in shooting weakly at Grbic instead of playing in Nunez.

Deep into additional time Jayden Bogle forced Kelleher into a save low down by his left-hand post and it seemed a brief respite until Gus Hamer outjumped Bradley with his header deflecting off the defender and through the legs of Kelleher in the 58th minute.

Andy Robertson and Harvey Elliott, on his 21st birthday, were already stripped to come on before the goal but the departure of leading scorer Mohamed Salah was a surprise, even more so to the Egyptian who did not make eye contact with Klopp as he departed.

However, the tactical adjustment, also made with one eye on Sunday’s trip to Manchester United, worked as the hosts began to find more room down the sides as Virgil van Dijk had a header palmed wide and Bradley volleyed Elliott’s deep cross into the side-netting.

But it was another botched clearance, this time by Anel Ahmedhodzic, which created the winner as the defender’s attempt to hoist the ball clear of his own penalty area deflected off Diaz to fall invitingly for Mac Allister to rifle home his fourth in five games.

Mac Allister the hit the crossbar with a free-kick before Gakpo finished things off in additional time.