The win was slightly marred by an injury to star defender Virgil van Dijk, who was taken off in the second half with an apparent rib injury.
Relentless Liverpool march on.
Some fans also felt the Cameroon worldwide has looked rusty this season, far below the high standards he set when he first joined the Anfield club. "But he is still a threat, has fantastic situations in both games and he is in good shape".
However, with the Holland worldwide unlikely to play in the midweek Carabao Cup game at home to Chelsea, the centre-back has a full week to recover before the top-of-the-table clash at Stamford Bridge.More news: Wolves, KAT agree to super-max extension
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And the pundit also believes Liverpool have their best chance of winning the league since Kenny Dalglish led them to victory in 1990.
21' - GOAL! Liverpool 2-0 Southampton (Matip). The Reds are cruising now. Salah was applauded after ending his "goal drought"...
Liverpool boss Jurgen Klopp says the club "do not expect" Mohamed Salah to replicate his goalscoring form of last season - and joked his forward is facing "a crisis". Despite initial claims from the Swiss playmaker, his dead ball didn't cross the line and it was definitely Salah's goal.
The result extended Liverpool's 100 per cent start to the campaign to seven matches in all competitions.
Defensively it is equally impressive as they have not conceded a home league goal in 12-and-a-half hours, extended over eight matches - their longest sequence since a run of nine in 2006-07.