Salah has scored on last seven appearances at Old Trafford
The Egyptian set up two Luis Diaz goals in the first-half and then got himself on the scoresheet for the seventh consecutive time at Old Trafford, that strike just before the hour mark effectively sealing victory for Liverpool on a dream afternoon.
The Reds join Manchester City on nine points heading into the international break, with the Arne Slot era getting off to a perfect start.
It is back-to-back defeats for United, though, leaving them 14th in the Premier League table, and the pressure is swiftly back on Erik ten Hag, as it was for much of last season.
Ten Hag brought Matthijs de Ligt, Joshua Zirkzee and Alejandro Garnacho into the starting lineup, while Liverpool went for an unchanged side in their attempt to build on opening wins over Ipswich and Brentford.
Within seven minutes they appeared to be off to the perfect start, Trent Alexander-Arnold’s strike deemed to have crossed the line after a quick glance from referee Anthony Taylor to his watch. However, just as Alexander-Arnold had sprinted off to kiss the camera and emulate Steven Gerrard’s celebration on this ground, VAR checked for offside and ruled it out.
It was fairly cagey from that point for much of the opening half an hour, both sides sloppy on the ball and neither able to take real control. The match turned in Liverpool’s favour ten minutes before half-time, and there it remained.
Casemiro played a dreadful pass and Liverpool swiftly countered, the ball played to Salah to dink a cross to the back post and Diaz was there behind Dominik Szoboszlai to head home.
The Liverpool duo combined for the second before half-time, and Casemiro once again played his part. This time the Brazilian was robbed of the ball as he strolled forward, toppling to the ground in slow-motion as the visitors again pounced.
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Salah played a brilliant ball into the middle, where Diaz was on hand to sweep a first-time finish beyond Andre Onana.
Casemiro, to nobody’s real surprise, did not emerge for the second-half, Ten Hag turning to Toby Collyer almost out of necessity.
But it did little to slow Liverpool’s charge, as Slot’s men made it three within ten minutes of the restart. Kobbie Mainoo lost possession, far too weak as Alexis Mac Allister shrugged him off the ball, and Szoboszlai played in Salah to once again celebrate in front of the Old Trafford away end.
The Egyptian was very nearly doing so again seconds later, after Lisandro Martinez played the ball straight to him from kick-off, but Salah on this occasion could only blast over.
Zirkzee had two good chances to reduce the deficit, both from Marcus Rashford crosses, but could not take either. The main positive for United was that no further damage came at the other end.
Szoboszlai attempted, quite literally, to walk the ball into the net rather than lash home from ten yards out, a sign that complacency was creeping in, but the emptying stands told the story of what was a painful afternoon for all those in the United camp.