After Trent Alexander-Arnold had a goal disallowed for an early opening due to a video assistant referee review, the visitors took the lead 10 minutes before halftime on a header by Luis Diaz.
Seven minutes later, after being set up by an exquisite move from Mohamed Salah, Diaz doubled his score with a low finish into the bottom corner.
In the Premier League, the Egyptian scored United's twelfth goal of the match in the second half as Liverpool capitalized on another midfield error by the Red Devils to increase the lead.
With this win, Liverpool and Manchester City are the only two teams with perfect records after three matches. United are in fourteenth place with three points going into the international break.
How the match unfolded
In the sixth minute, Liverpool believed they had hushed the Old Trafford fans after Diogo Jota had already missed the target with a flash.
After a brilliant passing play, Alexander-Arnold finished it off at the back post, beating Diogo Dalot, who was on the line. The goal was first given the green light, but it was later reversed due to a video assistant referee's determination that Salah had been offside throughout the buildup.
But in the 35th minute, Slot's team took the lead when Salah crossed the ball from Casemiro, and Diaz nodded at the far post.
Salah was once again the architect, setting up Diaz for a brilliant finish after Casemiro was dispossessed, and the two collaborated to increase the Reds' lead three minutes before halftime.
After 56 minutes, as United were starting to lose control of the game, Salah scored a goal by finishing into the bottom right corner after a dispossessed Kobbie Mainoo in midfield.
Despite avoiding more harm, the Red Devils could not score a comeback when Joshua Zirkzee wasted their two best late-game chances.
United lost midfield battle
Liverpool again mercilessly exposed United's much-maligned midfield, adding fuel to the fire that has become the Red Devils' lack of tactical identity throughout Erik ten Hag's tenure as manager.
Zirkzee and Bruno Fernandes tried to take the lead in the first exchanges. But Liverpool's Virgil van Dijk and Ibrahima Konate could command the midfield and advance the ball quickly since their opponents were not on the same page.
After being involved in both of Diaz's goals in the first half—the first via a sloppy pass and the second through a straightforward loss of possession—Casemiro will once again face criticism.
He was substituted by 20-year-old Toby Collyer at halftime, ending his dismal adventure before it started.
When Salah scored his tenth goal in nine matches at Old Trafford, Alexis Mac Allister snatched his pocket, and the Reds could go back on the offensive again, although Mainoo was also to blame.
With the final whistle blown by Anthony Taylor, boos resounded across Old Trafford, and Ten Hag had something to think about over the international break.
Liverpool's most challenging match under Slot thus far was at Old Trafford, but the Dutchman expertly navigated the challenge.
In contrast to United's Jose Mourinho, Slot has seemingly already imprinted his style on his team. They continue the expansive and exciting game that Jurgen Klopp established during his illustrious nine years at Anfield.
Liverpool failed to acquire a defensive midfielder during an unusually quiet transfer window, which may have been the missing link in their jigsaw. However, Ryan Gravenberch's recent performances have shown that he has the necessary qualities to play that role for the remainder of the season.
Salah became only the second player in Premier League history to score ten goals at an away venue, joining Alan Shearer at Elland Road, and Diaz were Sunday's outstanding performers.
Liverpool's new head coach will keep them on top of this classic matchup, and their early season performances may raise eyebrows in Manchester.
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