The Reds came into this game on the back of four consecutive defeats and Jurgen Klopp was under pressure to guide his side back to winning ways.
Both teams had key players unavailable due to injuries but they managed to put on an impressive showing in the first half.
Liverpool had the better chances of the two sides but the likes of Roberto Firmino failed to convert from close range.
With both teams heading into half time without having scored a goal, the Reds were expected to come out snarling in the second half.
Midfielder Curtis Jones took advantage of a poor clearance from Sheffield United to slot the ball into the bottom corner to give his side the lead in the second half.
Roberto Firmino’s deflected shot doubled Liverpool’s advantage and the Reds managed to hold on defensively to claim all three points.
Liverpool are now sixth in the Premier League table with 43 points and they are just two points adrift of 4th placed West Ham.
The Reds will be desperate to finish in the top four this season and it will be interesting to see if they can build on this win and put together a winning run now.
Adrian produced an impressive goalkeeping performance for the Reds in the absence of Alisson and Kelleher.
It will be interesting to see if the Spaniard keeps his place in the starting lineup next time out.
Meanwhile, Sheffield United remain bottom of the table with just 11 points so far.