Mohamed Salah settled the scores with a stoppage time insurance goal after Virgil van Dijk had given the unbeaten league leaders a first half lead.
The Reds still have a game in hand against West Ham United next week while the Red Devils stay fifth, five points adrift of Chelsea in fourth.
In a mini-battle between the world’s two most expensive defenders, Virgil van Dijk outjumped Harry Maguire to head Trent Alexander-Arnold’s corner into David de Gea’s net for the game’s opening goal in the 14th minute.
Liverpool thought they had scored a second ten minutes later but Van Dijk was adjudged to have fouled De Gea in the buildup to Roberto Firmino’s curling effort and the goal was quite rightly ruled out.
De Gea came to United’s rescue on the cusp of halftime when he blocked Sadio Mane’s low shot from the edge of the box with his legs.
Liverpool returned from the break looking to extend their lead and it was captain Jordan Henderson who came closest with rasping drive outside the box, which required the full stretch of De Gea to tip onto the post.
A brilliant one-two between Anthony Martial and Andreas Perreira sent the Frenchman in on the Liverpool goal, but the former AS Monaco forward smashed his effort over the bar with only the goalkeeper to beat.
As United chased an equaliser late into the game, they left gaps at the back which goalkeeper Alisson Becker duly exploited with a long pass to Mohamed Salah, who ran the entire length of the pitch with Daniel James for company before slotting past De Gea to seal all three points.
