"We’ve conquered all of Europe" rang around the stands ahead of kick-off, but it was domestic domination on the fans' minds after a fascinating title race took another turn with rivals Manchester City and Arsenal both tasting triumph on Wednesday evening.
With the latter leapfrogging the Reds into pole position, Liverpool were predictably hungry, but it was the visitors who should have led within 45 seconds when James McAtee inexplicably hit straight at Caoimhin Kelleher from just six yards out.
Characteristically under Klopp, the Reds were unbothered by any alarm bells and marched forward; fighting fire with fire. Darwin Nunez was at the centre of their best work, and it was his willing runs that led to Liverpool’s opener.
Chasing down what appeared to be a lost cause, the Uruguayan forward’s pressure on visiting keeper Ivo Grbic saw the stopper smash the ball into his midriff and fly into the net.
The intensity of the hosts’ attacks grew in strength after the opener, and Chris Wilder was likely content to see his players trudge down the tunnel with just a one-goal deficit at half time.
With the hosts having lost just one of their previous 39 home league matches against promoted clubs, the Sheffield United faithful knew the scale of the task ahead.
Those fans would have been happy to witness the bravery displayed by their relegation-threatened side before they were rewarded, in fortunate circumstances, shortly before the hour mark.
A flighted ball from McAtee was met by the head of Gustavo Hamer before a clumsy attempted clearance from Liverpool youngster Connor Bradley saw the ball slip through the legs of Kelleher.
Tension had suddenly filled the Merseyside air with Liverpool desperate for redemption. They saw several chances, most notably Andrew Robertson’s volley which flew past the post.
But anyone who has watched the Reds this season will have become accustomed to late winners, and, with the Kop holding its collective breath, upstepped Alexis Mac Allister to laser home in spectacular fashion from 25 yards.
Liverpool's tails were now firmly up, and, after going close on numerous occasions, Cody Gakpo nodded home in the final minutes to seal the contest.
A cruel night for a valiant Sheffield United - their top-flight status now hangs by a thread. Contrastingly, another late victory for the Reds will only enhance their belief that they can lift the Premier League trophy in May, despite having kept just one clean sheet in their last nine league games.
Flashscore Man of the Match: Alexis Mac Allister (Liverpool)
