In the week in which they were dethroned as Premier League champions, Liverpool responded with a performance akin to last season as Jurgen Klopp recorded his first win at Old Trafford to go within one point of fourth-placed Chelsea.
The fixture, re-arranged after fan protests 10 days ago led to the match being postponed, took place after a massive security operation foiled another attempt at disruption from protesters.
After spending seven hours inside the ground having arrived early to avoid attempts to block their bus. United took a 10th- minute lead when Bruno Fernandes’s shot was deflected past Alisson by the outstretched leg of Nathaniel Phillips.
Liverpool drew level in the 34th minute when Diogo Jota flicked in a low shot from Phillips and the visitors took the lead on the stroke of half-time thanks to Roberto Firmino’s back-post header.
The Brazilian extended the visitor’s lead two minutes after the interval when, after sloppy play from United, Alexander-Arnold’s shot was spilled out by goalkeeper Dean Henderson and Firmino slotted home.
Marcus Rashford pulled one back for United, with a confident finish after a smart exchange with Edinson Cavani, but as the home side pushed forward in search of a leveller, Mohamed Salah wrapped up a positive night for the Merseysiders with a fine finish after a swift break.
Liverpool moved above West Ham into fifth place on 60 points. Klopp’s side are four points behind Chelsea, who occupy the fourth Champions League slot but have a game in hand. United stayed second in the table, 10 points behind champions Manchester City.