Sadio Mane and Roberto Firmino were the goalscorers in either half for Jürgen Klopp’s side, who have sandwiched their UEFA Super Cup success with the maximum six points in league football.
Here are five talking points from St Mary’s…
Sadio delivers again
It’s fair to say the opening 45 minutes on the south coast were pretty forgettable, with neither side able to find a real rhythm or gain momentum.
But the game’s breakthrough was well worth waiting for, at least for Liverpool, as Mane produced an exquisite strike to put his team in front in first-half stoppage-time.