Liverpool boss Jurgen Klopp made three changes to the Liverpool line up to help secure all three Premier League points inside the first half.
Joel Matip was making his first start of the season, replacing Gomez, while Xherdan Shaqiri made his first competitive start in his Liverpool career, to give James Milner a breather. Roberto Firmino came back into the starting line up at the expense of Daniel Sturridge.
And Matip and Shaqiri were involved in the three first half goals that effectively rendered this game as done.
First half domination
Liverpool were typically dominant in the early stages of the game. Mo Salah was today occupying a central position with Shaqiri playing the advanced midfield role just behind him.
In the 10th minute the reds opened the scoring, with a bit of help.
Mane and Shaqiri combined on the left side of the area and Shaqiri attempted a curling shot into the far corner. It took a deflection off what appeared to be an arm of a defender before Hoedt stuck out a foot to clear and diverted it past his own keeper to make it 1-0.
Ten minutes later the lead had doubled.
Trent Alexander-Arnold swinging out a corner in front of the Anfield Road, and Joel Matip rose highest and with a powerful header slammed it in to the ground and into the net.
There as an opportunity for the tricky Salah in the area when he spun and backheeled a shot that went narrowly past the post.
Southampton tried to force their way back in but Liverpool's defence were in control and as the half approached it's conclusion the reds were awarded a free kick outside the area.
A thundering attempt by Xherdan Shaqiri rattled and rebound off the crossbar and Mo Salah was the first man on hand to tap in for his third goal of the season.
Half time changes
At half time Xherdan Shaqiri was replaced by James Milner. He had taken a big hit from Oriel Romeu in the first half, which landed the Southampton player with a yellow card, and there were suggestions it was a precautionary substitution.
Virgil van Dijk also had to go off early in the second half after appearing to injure his rib. Joe Gomez a more than useful player to have on the bench.
Both van Dijk and Shaqiri appeared on the bench after their substitutions, which suggests that the injuries are not too serious.
The second half lacked the intensity of the first half with Southampton understandably resigned to their fate. Naby Keita got a 20 minute run out for the reds who strolled through the final period of the game.
Mo Salah was flagged offside after putting the ball in the net late on. James Milner had two opportunities denied in the build up to the disallowed goal.
Tougher tests await the reds who face Chelsea twice in the next week as they get their domestic cup campaigns underway.
Liverpool return to clear top of the Premier League with fellow 100%'ers Chelsea in action at West Ham on a Premier League Sunday.