The hosts could have taken all three points, Gerard Deulofeu having an early goal ruled out for offside while a strong penalty appeal from Will Hughes was denied by the referee.

But Salah hit a first-time finish through the legs of goalkeeper Ben Foster, scoring his fourth goal in five Premier League games before Alexander-Arnold’s wonderful free-kick put the visitors in control.

Their win was marred, though, when captain Jordan Henderson was dismissed with eight minutes to go, meaning will be banned for next weekend’s Merseyside derby, although Firmino added a late third.

Watford had a goal ruled out in the second minute, Deulofeu running on to Troy Deeney’s pass to beat Alisson with a smart finish, but he was offside.

Liverpool added Xherdan Shaqiri to a front three of Salah, Firmino and Sadio Mane – who signed a new deal on Thursday – but it took them 38 minutes to record a shot.

Firmino found space and fired off a low effort which Foster held well, Roberto Pereyra then testing Alisson’s reflexes at the other end before the Watford goalkeeper kept out Salah’s header.

Referee Jon Moss waved away Watford penalty appeals when Hughes went down under Andy Robertson’s rash challenge early in the second half.

Salah should have opened the scoring, slotting his finish through Foster’s legs but wide of the far post, but he did break the deadlock soon after.

Firmino fed Mane through the left channel and the Senegal star pulled back a low cross for Salah, whose finish lacked power but was directed well enough to beat Foster.

Alexander-Arnold put Liverpool’s firmly in the ascendancy with 14 minutes to go, curling a fantastic 25-yard set piece out of Foster’s reach for his first Premier League goal of the year, before Henderson was sent off for a second yellow card late on.

And Firmino added his name to the scoresheet in the 89th minute, nodding in from close range after Foster denied Mane.