The Reds had to twice come from behind, with Harry Maguire's first-half header and a Bruno Fernandes penalty answering Blades' efforts from Jayden Bogle and Ben Brereton Diaz.
And Erik ten Hag's men secured the three points in the final 10 minutes of normal time, as Fernandes brilliantly curled home from 25 yards and then set up Rasmus Hojlund for a fourth.
That moved the skipper on to 26 goal involvements for the campaign, more than any other Premier League midfielder has managed, and he was once again your Man of the Match, making it three straight wins after topping the polls against Bournemouth and Coventry too.