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Will Smallbone capitalised on a mix-up between Alisson and Virgil van Dijk to put the Saints 1-0 up against the hosts before half-time.
Liverpool were sluggish in the first 45 minutes and fashioned very few chances against their bottom-of-the-league opponents.
But three half-time substitutes helped bring some pace to the play and by the 54th minute, the Reds led 2-1 after Darwin Nunez’s finish and a Mohamed Salah penalty that had been won by the Uruguayan.
Hardly bothered second half though.
Kostas Tsimikas - 5
Seemed to struggle for rhythm and was brought off at half-time after picking up a cynical yellow card.
Ryan Gravenberch - 6
Some good flashes but largely below his best level.
Not as energetic as his previous outings, rather understandably.
Mohamed Salah - 7
Struggled first half but improved after half-time and scored the penalties to make it 2-1 and 3-1 to Liverpool.
His pressing also helped lead to Liverpool's second penalty.
Substitutes
Harvey Elliott - 7
Brought on at half-time after his PSG winner in midweek.
Immediately forced a good save from Ramsdale and frequently involved, taking several well-struck shots on goal.
Andy Robertson - 7
Another of three half-time subs and was much livelier than Tsimikas as he bombed down the left-hand side.
Alexis Mac Allister - 6
The third of the subs at the break, brought more composure to the midfield.
Diogo Jota - 6
Replaced game-changer Nunez after 68 minutes.