Liverpool were without their custodian Alisson Becker, who was on compassionate leave after the death of his father, which meant Adrian started between the sticks.
The reigning champions uncharacteristically began the match in a quiet manner as they posed no threat in attack, giving Sheffield United the opportunity to run at their defense.
Oliver Norwood drilled in an excellent free-kick which was met by David McGoldrick, however, Adrian did enough to keep the ball outside his goals.
This seemed to have awakened the sleeping Reds, who soon went searching for the opener.
Brazilian striker Firmino drove deep into the box and into a shooting position, however, his shot was blocked by an inspired Aaron Ramsdale.
Ramsdale continued his fine outing in front of goal, keeping the Blades in the game by denying Curtis Jones, Mohamed Salah, Georginio Wijnaldum and Trent Alexander-Arnold, who looked to capitalize on a defensive mistake by Ethan Ampadu.
Both teams went into half-time at 0-0
However, three minutes into the restart, Alexander-Arnold drilled in a cross for Curtis Jones to fire home his second Premier League goal for Liverpool.
Sheffield hit back in search of a way back into the game, but when McBurnie was presented with another glorious opportunity, he fluffed his finish.
Liverpool soon doubled their advantage five minutes after the hour mark when Firmino, Jones and Mane linked up brilliantly before the Brazilian drilled home his effort.
After a review, the goal was awarded as Kean Bryan's own goal after it showed that Firmino’s shot was going out wide.
Liverpool did not drop the tempo as they continued to look to extend their lead and did just enough to hold on to the clean sheet.
The result now sees Liverpool move three points above bitter rivals Everton, with whom they could be tied with on points should the Toffees grab a win against Southampton.
Sheffield United 0-2 Liverpool: 5 Talking Points
#5 Liverpool win without Alisson
Brazilian first-choice goalkeeper Alisson Becker was out on leave after the death of his father.
While Adrian was rarely disturbed by the Sheffield United attack, he made three brilliant saves for Liverpool. Adrian, who has proved to be unreliable on occasion, was making his first appearance since the 1-0 win over Ajax in September.
In the run-up to the Ajax game, Adrian conceded a shocking nine goals in two matches as Liverpool fell to a 2-2 draw with Everton and a humiliating 7-2 defeat to Aston Villa.
#4 Curtis Jones stars for Liverpool
The Liverpool academy graduate was a standout performer against Sheffield as his 48th-minute strike gave the visitors a one-goal lead.
The youngster showed great maturity and composure in the center of the park for Liverpool as he kept the ball moving in midfield and in possession while also contributing brilliantly in defense.
His positional play and awareness were simply superb as he found pockets of space all game while linking up with the frontmen.
Jones grabbed his second goal for Liverpool when he drilled in a brilliant side-footed strike after a cross from Alexander Arnold.
Sheffield players protested the goal, claiming the ball had gone out of play in the build-up but after consulting with VAR referee Jonathan Moss confirmed the goal.
Jones has made 19 appearances for Liverpool, staring 11 of them this season.