Firmino's 20th goal in all competitions put Liverpool ahead after just six minutes from Salah's pass before Firmino returned the favour with a stunning flick, setting up Salah for his 29th of the season.
How did the players fare individually?
Perfect return for the man who had all eyes on him
Loris Karius (8) - Another solid display from the German who played a crucial role in the Reds being two up at half-time. Excellent stops from both Pierre-Emile Højbjerg and James Ward-Prowse in the first half and his quick thinking kickstarted the move for the opening goal.
Trent Alexander-Arnold (7) - Southampton looked to get behind the space he left but the youngster dealt with that very well, So exciting going forward, with one excellent ball down the line to Salah to showcase why he deserving of being the Reds no 1 right back, and looked dangerous as the extra runner.
Virgil van Dijk (9) - All eyes were on the worlds most expensive defender and the Dutchman was unfazed by the predictable unwelcome return to St Mary's from the home support, and similarly unperturbed by Guido Carrillo on the pitch. Commanding, won his battles and showed some nice passes. A perfect return for the 26-year-old.
Joel Matip (6) - It was a difficult first half from the Cameroonean and he didn't make his chances of being Van Dijk's permanent partner much good from a defensive perspective, though improved in the second half. Lost his balance a couple of times going backwards, but did start the move for the second. Booked.
Andy Robertson (6.5) - Usual reliable self-going forward but was unfortunately caught out with a back post cross which Hojbjerg failed to convert in the first half, and his distribution was poor. Always gives everything though and can't be faulted for that.
Midfield three solid once again
Emre Can (6.5) - The captain on the day was suspended for the trip to Porto, so the German was always going to start this game – and did well. Held his shape in midfield well and looked good when moving the ball quickly, though he perhaps should have done it more.
Gini Wijnaldum (7.5) - Very good performance from the Dutchman as he served a reminder of what he does in this midfield. Popped the ball off well during counter attacks and served as an extra body in midfield when needed. Deserves to keep his place in the midfield three.
Alex Oxlade-Chamberlain (6.5) - Helped set up the opener with an excellent ball to Salah and chased everything. Functional rather than fantastic, but didn't need to be anything other during his hour on the pitch.
Salah and Firmino unplayable again
Mohamed Salah (9) - Without a doubt the signing of the season. Unplayable for the opening 15 minutes and teed up the Firmino opener, then once more exploded into life to give Liverpool the two-goal cushion. Always an outlet, always running, always scoring. Could have had more. A phenomenal addition.
Sadio Mané (6) - It didn't quite go for the Senegalese star on his return to St Mary's and perhaps was guilty of trying a little too hard. Decision-making wasn't quite there and didn't make the most of promising positions. However, still showing signs of getting back to his best.
Roberto Firmino (9) - Bagged goal number 20 of the season with a well-taken finish, but he pulled out the move of the match on the stroke of half-time with a back heel that was begging to be scored by Salah. Worked his Brazilian gonads off and was phenomenal throughout.
Subs help see out win
James Milner (7) - Gave the midfield could fresh impetus after an hour and always looks his best in midfield when it goes a little bit, well, bitty.
Adam Lallana (6) - Could have scored against his former club with a curling effort.
Dejan Lovren (N/A) - Wasn't on long enough to warrant a rating on his return to St Mary's.