Liverpool conceded a penalty in the 11th minute. Olly McBurnie was fouled by Fabinho right on the edge of the penalty area - prompting the referee to award the visitors a free-kick right outside the area. Upon review, the referee deemed that the foul occurred on the line.
Sander Berge stepped up and sent Alisson the wrong way - giving the visitors the unlikeliest of leads at the home of the champions.
Liverpool found the equaliser in the 41st minute. A cross from the right was met by the head of Sadio Mane, who forced a desperate save from Aaron Ramsdale. The keeper could only parry the ball weakly though, allowing Roberto Firmino to nip in and score from the rebound.
The Blades had an excellent opportunity three minutes after the interval. John Lundstram's cross was knocked down by Berge for George Baldock, who charged onto the ball and hammered a powerful volley across goal, which was deflected on its way through for a corner.
The Reds took the lead in the 64th minute. It was a simple goal for the hosts, as Mane's cross from the left found the head of Diogo Jota - who was allowed to peel off the back of Enda Stevens and nod it past Ramsdale.
The hosts came close to a third in the 82nd minute. A spectacular turn on the edge of the penalty area got Salah by his marker in possession, but his deft chip over a diving Ramsdale ricocheted off the post and rolled back into the arms of the grateful goalkeeper.