After being in midweek EFL Cup action, both sides reverted to their winning line-ups from last weekend in the Premier League.
A tame first half almost ended in drama ahead of interval when Liverpool broke clear, with an overlap on both sides.
However, Roberto Firmino delayed his pass, eventually finding Sadio Mane, who struck the foot of the post. The ball fell back to Firmino although John Fleck was on hand to tackle the ball to safety.
Liverpool tweaked their formation at half-time, pushing Fabinho back into defence as a sweeper, but soon abandoned those plans as the Blades dropped deep into their own half.
Mane had a penalty shout turned down when John Lundstram appeared to catch him after the Senegalese had crossed and it appeared as if the pressure was starting to tell on the home side.
Oliver Norwood did have an effort for United well saved by Adrian before the decisive moment came shortly afterwards on 69 minutes.
A scramble in the Blades box saw the ball fall to Georginio Wijnaldum. The Dutchman fired a decent effort towards goal but goalkeeper Dean Henderson looked to have it under control, only for a lapse in concentration to result in the ball squirming through his arms and into the empty net.
Chris Wilder did his best to keep his troops calm and they had half-chances through the likes of Leon Clarke and Oli McBurnie.
But the equaliser was not forthcoming and the Reds’ perfect start to the Premier League season continued.