Anfield was fraught, Liverpool increasingly frantic and Sheffield United were surprisingly holding a door open to Arsenal and Manchester City in the title race. Alexis Mac Allister slammed it shut magnificently. Another decisive contribution from the World Cup winner returned Jürgen Klopp’s team to the Premier League summit as Liverpool held their nerve and their advantage yet again.

Leaders thrive in the heat of a title race and the calm, unassuming but supremely gifted Argentina midfielder is relishing the responsibility of driving Liverpool towards the second Premier League trophy of the Klopp era. Mac Allister has been involved in a Liverpool goal in the last six matches, scoring four and delivering four assists, and his latest strike was the sweetest in terms of execution, timing and importance. Gary McAllister, appropriately enough, was looking on as the 25-year-old found the top corner of Ivo Grbic’s goal to restore Liverpool’s lead after Conor Bradley’s own goal had drawn Sheffield United level and threatened an unexpected slip-up.

Related: Liverpool 3-1 Sheffield United: Premier League – live

Chris Wilder’s relegation-threatened team battled impressively and defended resolutely with the notable exception of the goalkeeping error that gifted Darwin Núñez the opening goal. They were undone by another stirring Liverpool finale, however, with Mac Allister’s the 25th and Cody Gakpo’s 90th-minute header the 26th goal that Klopp’s side have scored in the last 15 minutes of a game this season. Gakpo’s was also the 80th goal that United have conceded this season. “A World Cup winner and a world-class finish,” as the United manager described Mac Allister’s defining moment.

The contest was far from the Liverpool cruise that many anticipated between the league’s top and bottom clubs, although the hosts were assisted in their return to the summit by a gift of an early goal from Grbic. The visiting goalkeeper’s mistake was bad enough in isolation but, to Wilder’s added dismay, it also served to thoroughly undermine a decent start by the league’s basement club.

United came close to opening the scoring inside the first minute when Jack Robinson’s long throw was flicked into the path of James McAtee. With the Liverpool defence caught cold and the on-loan Manchester City forward all alone at the back post it needed a point-blank save from Caoimhín Kelleher to prevent a shock early lead.

Wilder’s deep-lying team were also resisting Liverpool defensively until the Anfield academy graduate Robinson, who remains the youngest player to appear for the club in the league, played a routine back pass to his keeper. Grbic took a touch and then an age over his clearance, casually taking three steps back and searching out targets before striking the ball. He succeeded only in hitting the incoming Núñez on the thigh and turned around in horror to see the ball bouncing into an unguarded net. Luck was on Liverpool’s side but Núñez deserves full credit for setting off in pursuit of a remote chance as soon as Robinson played the back pass.

The breakthrough unsurprisingly deflated the visitors for a spell. Liverpool controlled proceedings and dominated possession but a slender lead, and a fortunate one at that, kept Klopp and Anfield on edge. The continued cries of “Shoot” whenever Joe Gomez had the ball in the final third once again riled the Liverpool manager, who made it clear to supporters in the Main Stand behind him that this was no time for frivolity.

Several promising counterattacks for United early in the second half added to Klopp’s anxiety, and his fears were realised when one resulted in a shock equaliser. Gustavo Hamer instigated the break by releasing McAtee down the right before sprinting towards the Liverpool penalty area. When the forward’s deep cross arrived at the back post, and just over Ben Brereton Díaz, Hamer’s header back across goal struck Bradley on the shin and rolled through the legs of Kelleher.

Anfield was stunned into silence. And left perturbed when Klopp responded by withdrawing Salah seconds later.

With passes going astray, crosses sailing out of play, Ibrahima Konaté temporarily injured and the visitors defending resolutely, Liverpool were in danger of squandering a glorious opportunity to maintain their lead at the top of the table. But then, as so often, Klopp’s team staged a vital recovery.

Andy Robertson, part of the double substitution that followed Bradley’s own goal, was instrumental in the late improvement and Mac Allister’s precious winner.

It was his low cross that resulted in a spot of pinball inside the United penalty area and a deflection that teed up the Argentina World Cup winning midfielder 20 yards from goal. Mac Allister connected perfectly, driving his shot so cleanly and powerfully into the top corner that Virgil van Dijk had his arms raised in celebration before it crashed into the net. Anfield, previously so tense, went wild. A stunning and significant moment in the title race.

Mac Allister was unfortunate not to grab a second goal with a 25-yard free-kick that struck the bar. Robertson did provide his second valuable contribution when sending an inch-perfect cross on to the head of fellow substitute Gakpo in the 90th minute. Gakpo steered his header into the bottom corner of Grbic’s goal and, finally, Liverpool were back in pole position.