But as the home side went in search of a goal they left themselves open to the devastating threat of a Liverpool counter-attack.
And in the 71st minute former Saints man Sadio Mane left Cedric on the floor to break away before finding Firmino who produced an excellent stop from McCarthy in goal.
The goalkeeper’s parry fell at the feet of Salah who looked nailed on to notch his second of the game but he could only rifle his shot into the side netting.
With the Southampton back four tiring, the Reds continued to run them ragged and Mane nearly scored at his former ground but was beaten by the angle.
Mane’s former Saints teammate oAdam Lallana then had his turn to come close to adding Liverpool’s third in the 85th minute.
Salah was involved again as he linked up with Lallana to leave the winger able to get his effort away but he could on watch on as it drifted inches wide.
The defeat leaves Saints deep in relegation danger and raises fresh question marks over the future of manager Mauricio Pellegrino.