On the back of being bumped down to second place by Arsenal, the Reds cut tepid figures in the first half of their clash with the basement boys, but a freak Darwin Nunez goal was enough to send the hosts into the break a goal to the good.
Conor Bradley's own goal gave the hosts a harsh reality check, but a rocket from Alexis Mac Allister saw the hosts poke their noses back in front, before Cody Gakpo erased any lingering doubt to ensure that Liverpool would remain in charge of their title destiny with a two-point lead over the Gunners.
With Wataru Endo not risked after taking a knock in the beating of Brighton & Hove Albion, Ryan Gravenberch was reinstated to the Reds' XI, which otherwise had a full-strength feel to it.
However, the visitors were fired up from the off and handed their hosts a major scare within 40 seconds of kickoff, as James McAtee ghosted in at the back post to meet a free kick but was thwarted by Caoimhin Kelleher.
McAtee's early opportunity was a serious wake-up call for Jurgen Klopp's crop, who started uncharacteristically sloppily but quickly wrestled back control of the game and began to put the Blades backline under pressure.
Ivo Grbic was first called into action in the sixth minute, making a relatively routine stop to tip Mohamed Salah's 20-yard attempt over the top, before a couple of inviting deliveries from Bradley went unanswered.
Nevertheless, Liverpool's pressure would eventually tell in the 17th minute, albeit in bizarre circumstances, as an airborne Nunez charged down a Grbic clearance, and the ball comically struck the Uruguayan's backline before trickling into an empty net.
After bagging his 20th Premier League goal in unorthodox circumstances, Nunez almost scored a more conventional second just four moments after breaking the deadlock, escaping several Sheffield United challenges but failing to get enough purchase on his shot to trouble Grbic.
Joe Gomez - still waiting to open his Liverpool account - was the next to try his luck, sending a swerving attempt wide with 23 minutes gone, the same fate that befell Mac Allister just after the half-hour mark.
Despite overwhelming Reds domination, their lead remained vulnerable as the half-time whistle approached, and Sheffield United were far from out of it; Jayden Bogle drew Kelleher into a crucial save down to his right in the fourth minute of added time.
As was the case in the opening 45, Liverpool were slow out of the blocks at the start of the second - albeit while still dominating the ball - and Sheffield United made the most of their hosts' lethargic demeanour in the 58th minute with a goal nearly as farcical as Nunez's opener.
A sublime move out from the back saw the Blades work the ball out to McAtee on the right, and the Manchester City loanee's cross to the back stick was knocked down by Hamer, whose header deflected off Bradley's shin and through the legs of Kelleher.
Klopp's men could not say that they were not warned, although a promising chance for Virgil van Dijk to immediately restore the hosts' lead arrived in the 65th minute, but Grbic quickly got down low to divert his header behind.
Sheffield United were doing their utmost to slow the game down as the last quarter approached, but their efforts were rendered futile with 13 minutes of regular time remaining thanks to a world-class strike.
Midfield maestro Mac Allister - brimming with energy all evening - got slightly lucky as the ball broke to him on the edge of the box, but there was nothing fortuitous about his first-time thunderbolt, which fizzed into the top corner to spark Merseyside mayhem.
The Argentine was inches away from registering another second-half stunner in the 85th minute, crashing a free kick off the upright, but the insurance goal would arrive four moments later, as Andrew Robertson's sumptuous cross was met by Gakpo to glance a header into the far corner.
A blockbuster trip to Old Trafford to face Manchester United is next on the Liverpool agenda for Sunday afternoon, a couple of hours before Chris Wilder's men - who remain last with a 10-point gap to safety - host Chelsea at Bramall Lane.