A first half penalty from Sander Berge gave the Blades a fighting chance at Anfield but goals either side of the break from Roberto Firmino and Diogo Jota secured all three points for the Reds.
Liverpool looked to overpower Chris Wilder’s side right from the off on Merseyside as John Egan cleared Sadio Mane’s effort off the line inside 60 seconds.
But despite struggling to live with Liverpool early on the visitors were handed a perfect opportunity after ten minutes.
Oli McBurnie was caught by Fabinho just inside the box and after a quick VAR check Berge calmly tucked home from the spot.
That goal injected some life into the Blades as McBurnie forced a smart stop from Alisson and Berge fired just wide.
But just as United were second best from kick off, Liverpool produced an equaliser out of nothing just before the break.
Aaron Ramsdale reacted brilliantly to keep out a header from Mane but Firmino stayed alive to cushion the rebound.
The Blades picked up the initiative after the break and Alisson was called into to beat out Oli Burke’s drive.
However, with United unable to turn their pressure into goals, Liverpool showed the clinical style of champions as Jota netted his first Premier League goal for the club.
Mane did brilliantly out wide to twist and turn and stand up a cross into the box with Jota arrived right on cue to power a header past Ramsdale.
United were forced to go for broke in the closing minutes as substitute David McGoldrick fired over the top before Salah wasted a golden chance to make it three.
Full time at Anfield it’s Liverpool 2 Sheffield United 1