However, they've also been dumped out of the FA Cup at the 4th round stage at home to bottom of the Premier League West Brom and have lost in the league away at 17th placed Swansea (they were bottom at the time).
Jürgen Klopp may choose to rest some of his star players ahead of Liverpool's Champions League match with Porto next week, but it will still be a strong side.
Liverpool have been particularly strong on their travels this season and have scored a league-high 34 goals.
Roberto Firmino and Mohamed Salah combined for both goals at the beginning and end of the first half as Liverpool returned to winning ways in the top flight, handing Jurgen Klopp his 50th Premier League victory as manager.
Southampton, they are on a decent run of six games unbeaten since opening the new year with a home defeat to Crystal Palace.
And this is how things stayed for the remainder of the clash, with the Saints struggling to create clear-cut goalscoring opportunities over the course of the second-half, whereas Liverpool could easily have added to their goal tally through the likes of Salah, Firmino and Sadio Mane.
"I enjoyed it a lot", Van Dijk said.
The centre-back turned out 80 times for the St Mary's side before his £75 million transfer to the Reds last month.
The pace that Liverpool have could cause a real issue for out back-line with Salah reeking havoc in the reverse fixture!
"If we were playing against towering defenders like Tony Adams and Jaap Stam and you were taking a set piece, you'd say "keep it away from him" or take the man away. I think we deserved the three points, [we got a] clean sheet, no injuries - [it was] almost ideal".
"It won't be a friendly game; they fight for everything, we fight for everything".