The Croatian has become known for making errors in big games this season and has struggled to hold down a place in Jurgen Klopp's side. The midfielder curled a fine ball over the top of Liverpool's defence and to Pierre-Emile Hojbjerg, who at the back post hesitated, allowing Karius to spread himself and then comfortably save the shot he eventually produced.
"We couldn't show what we are about, it was too much for us".
Karius, easily the busier of the two goalkeepers, was tested again just before the half-hour mark, halting Guido Carrillo's header from a James Ward-Prowse cross.
More of Liverpool's former Southampton contingent, Sadio Mane and Adam Lallana, should have rubbed salt in the home side's wounds when they both fired wide when clean through.
"It won't be a friendly game; they fight for everything, we fight for everything".
Liverpool have been particularly strong on their travels this season and have scored a league-high 34 goals.
Salah's strike was his 21st goal of the seaosn. For the Reds though, they saw a number of good chances spurned which may worry Klopp slightly.
The pressure on the hosts had increased with earlier victories for Newcastle and Huddersfield, over Manchester United and Bournemouth respectively, that left Saints back in the bottom three. Southampton by contrast are sinking into a desperate situation as they barely put up a fight on Sunday.
The arrival of Virgil van Dijk cast doubts over his long-term future at the club, with van Dijk and Joel Matip looking like the most natural centre-back pairing.
Van Dijk was jeered by the home support following his £75 million (Dh380m) move to Anfield last month, but got his revenge by shutting out a toothless Saints side who drop into the relegation zone.