The home side had the first notable chance of the game as Joe Gomez gave away possession before James McAtee saw his effort saved by Caoimhin Kelleher. Sheffield United came close for a second time after playing through the press, but Cameron Archer saw his strike blocked by Virgil van Dijk.
Liverpool managed to establish control in the match after those two moments, and eventually took the lead when Trent Alexander-Arnold's corner found Virgil van Dijk in space to volley past Wes Foderingham.
Mohamed Salah almost doubled the lead after the break with a volley in similar fashion, but this time the goalkeeper was equal to the shot. Substitute Darwin Núñez had the next best chance for the visitors after he was found by Alexander-Arnold, only to be denied by Foderingham.
Liverpool were patient and defended well to prevent counter-attacks as the Blades rarely presented a threat, though the game was finally put out of reach late on when Darwin Nunez won back possession before finding Dominik Szoboszlai who finished with composure in the 95th minute.
Liverpool were a threat from set-pieces and showed strong patience against a difficult defensive set-up. It's also another three important points in the title race as they keep the pressure on leaders Arsenal.
Liverpool started slowly and gave away two chances that might have been taken on another day.
7 -- Jurgen Klopp was decisive with his substitutions, including the moment when he took off an underperforming Mohamed Salah, while he also added control to his midfield with the introductions of Curtis Jones and Ryan Gravenberch.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK Caoimhin Kelleher, 7 -- The Republic of Ireland international had to be sharp in the first half as he saved well from on-loan Manchester City midfielder James McAtee. Remained alert for the rest of the game, but didn't have much to do until Sheffield United decided to attack in the final minutes.
DF Joe Gomez, 6 -- Joe Gomez defended his flank well, but struggled to make a consistent impact in attacking areas on his weaker left foot. Gave the ball away for Sheffield United's best chance of the first half.
DF Virgil van Dijk, 8 -- The Liverpool captain led by example with a number of excellent interventions, with one denying a shot inside the box from Cameron Archer, before scoring the opening goal with a well taken effort from a corner.
DF Ibrahima Konaté, 7 -- The 24-year-old transitioned the ball out of defence well and helped maintain solid structure in the back line. The France international star made a number of inventions, but was booked in the second half for a foul after hesitating on the ball before losing possession.
DF Trent Alexander-Arnold, 8 -- Some of his passes weren't quite at the expected standard in the first half, but he did pick up the assist from the corner that found Van Dijk for the opener. He looked back to his best from then on, and was unlucky not to get a second assist after an intricate pass to Darwin Nunez.
MF Wataru Endo, 7 -- A strong showing from the Japan international saw Wataru Endo break up play consistently in the middle of the park, while he often made the right decision with his passing, impressing when creating an angle by receiving the ball on the half turn before playing forwards.
MF Alexis Mac Allister, 5 -- A quiet first half saw him drift in and out of the game after suffering an early heavy challenge, though he did test the goalkeeper with an impressive touch and volley that required to be tipped over the bar. Replaced by Curtis Jones just before the hour mark.
MF Dominik Szoboszlai, 8 -- Dominik Szoboszlai was bright when on the ball in attacking areas, and there was a sense that something could happen when he was on the ball. Played in an intricate pass to Salah in the first half that the Egypt international should have done better with. Made the right decision during defensive transitions. He then put the game out of reach with a goal in the 95th minute from Nunez's pass.
FW Luis Díaz, 6 -- The Liverpool left-winger drifted wide and was often in space to receive diagonal passes. On the ball he was difficult to pick up, and was able to win fouls for Liverpool in promising areas.
FW Cody Gakpo, 6 -- The Netherlands international made impressive runs to create space for his team, and also stood out for his pressing ability to help Liverpool win the ball back quickly after losing it. Moved out to the left-flank when Luis Diaz was withdrawn.
FW Mohamed Salah, 5 -- Mohamed Salah could have taken more care with his shooting on the night as he seemed to rush his attempts in the first half. Unlucky not to score after a strong connection from a corner to force a strong save from Wes Foderingham. Substituted in the 67th minute for Harvey Elliott.
Substitutes (players introduced after 70 minutes get no rating)
MF Curtis Jones (replaced Mac Allister 59"), 6 -- On for Mac Allister close to the hour mark, and helped Liverpool control the game against a defensive Sheffield United set-up.
FW Darwin Nunez (replaced Diaz, 67"), 7 -- Darwin Nunez worked hard when introduced when leading Liverpool's press. Intelligent movement saw him latch onto Alexander-Arnold's pass, but he couldn't produce the finish to beat the goalkeeper. Excellent work for Liverpool's second goal saw Nunez win back possession before picking out Dominik Szoboszlai.
MF Harvey Elliott (replaced Salah, 67"), 6 -- Tried to make things happen when introduced. An effort from range was blocked, though he did provide an opening when finding Jones inside the box, but there were too many defenders around him to threaten the goal.
MF Ryan Gravenberch (replaced Gakpo, 86"), N/R -- On for the final minutes as Liverpool looked to play out the remainder of the game.