They were helped by two penalty awards in the first period, both converted by Robbie Fowler, for fouls on Steven Gerrard.
It was a Fowler spot-kick for a foul on Gerrard on the opening day of the season at Bramall Lane that led to Blades boss Neil Warnock suggesting the Liverpool skipper had dived.
And Warnock seemed to have a word with Gerrard when he came off at the break, but both spot-kicks were given for a tug and a push on the midfielder.
Liverpool added second-half goals by Gerrard and Sami Hyypia as they stepped purposefully from the glamour of their victory over Barcelona to a bread-and-butter destruction of the Yorkshiremen.
Boss Rafael Benitez was able to include goalkeeper Jerzy Dudek, making his first Premier League start of the season, and Fowler his third.
Javier Mascherano came in for his debut, while Craig Bellamy - villain turned hero with his Champions League display - was not even on the bench. Likewise Jose Reina, allowing Italian Under-21 goalkeeper Daniele Padelli his first taste of senior action as a substitute.
United were without suspended pair Keith Gillespie and Leigh Bromby.
Mascherano fitted into the expected holding role, leaving Gerrard to surge forward, but they were immediately confronted with a deep Blades defence and just Rob Hulse up front.
Benitez had opted for two wingers - Jermaine Pennant and Mark Gonzalez - against this system. Width being the best answer, he clearly felt, to a massed defence.
But Liverpool were given a helping hand as they dominated possession, with two penalties in a five-minute spell.
The first came on 20 minutes after Peter Crouch had been carried off with blood pouring from a head wound, courtesy of Hulse's boot.
But that was not the incident that made referee Steve Bennett point to the spot. Seconds earlier Rob Kozluk was spotted grappling with Gerrard, pulling him to the ground. After Crouch's eventual departure, Fowler stepped up to drive home the penalty.
And it got worse for the Blades. Dirk Kuyt was on as substitute for Crouch and with his first touch he headed the ball into Gerrard's path in the box, the Liverpool skipper being pulled back by Nick Montgomery.
Referee Bennett pointed to the spot again, and Fowler this time sent Kenny the wrong way for his third goal of the season.
All three have been from the spot, and all three for fouls on Gerrard against Sheffield United, the first on the opening day of the season at Bramall Lane.
Before the re-start, Kozluk was replaced by Colin Kazim-Richards. And the Blades had to make another change on 30 minutes when Chris Lucketti went off with an ankle injury, Chris Morgan taking over.
The Blades gave it a go at the start of the second half. Montgomery misdirected a header wide from eight yards and Dudek needed to rush from his line to dive at Stephen Quinn's feet.
But Liverpool were in control without being at full throttle. Gerrard fired a 20-yard shot wide and Fowler saw a header bounce wide from Pennant's cross, with Gerrard waiting behind him in a much better position.
Hulse had a close-range chip ruled out for offside, while at the other end Riise fired a fierce 30-yard shot over the angle.
On 66 minutes the Blades sent on another striker, Jonathan Stead for Quinn. But any thoughts of a Blades comeback were soon ended.
Liverpool made absolutely sure of the points with two goals in three minutes.
On 70 minutes when Pennant's corner hit Morgan in the box, Hyypia was on hand to fire the ball home off Kenny"s hands.
Then three minutes later a Fowler pass found Gerrard free in the box, and he drilled a fine shot into the far corner. Xabi Alonso replaced Gerrard before the re-start.
Daniel Agger came on for Jamie Carragher soon after, and United wasted their best chance of the game on 80 minutes when Hulse hit the bar from six yards following a Kazim-Richards cross.