United succumbed to a third Premier League defeat in four games as Jurgen Klopp’s side ran riot to humiliate Solskjaer’s men on their own patch.
Naby Keita opened the scoring inside five minutes and Diogo Jota doubled the lead before Salah took centre stage, scoring three times before Paul Pogba, on as a half-time substitute, was sent off to compound United’s misery.
Solskjaer had been boosted ahead of kick-off by the availability of Marcus Rashford and Bruno Fernandes, both of whom had been injury doubts, while Klopp opted for Jota over Sadio Mane and brought Ibrahima Konate into the side to partner Virgil van Dijk at centre-back.
Keita had the simple task of putting Liverpool ahead when he was slipped in by Salah after United’s press had been too easily bypassed and the home side were masters of their own downfall for the second goal, too.
Luke Shaw and Harry Maguire were involved in a defensive mix-up that allowed Keita to feed Trent Alexander-Arnold and the right-back’s cross was perfect for Jota to slide home.
Keita was involved in the third soon after, squaring for Salah to lift into the roof of the net, before the Egyptian added a fourth with a near-post finish deep into first-half stoppage time.
Solskjaer turned to Pogba at half-time in a bid to gain some control and limit the damage but within minutes of the restart Jordan Henderson’s magnificent pass put Salah in to lift over David de Gea and complete his hat-trick.
United thought they had pulled one back through Cristiano Ronaldo’s low finish but his effort was chalked off for offside by the VAR, who also then encouraged referee Anthony Taylor to review the pitch side monitor and upgrade Pogba’s yellow for a two-footed lunge on Keita to a red as United played the final half-hour with ten men.