The Portugal forward grabbed his first with less than two minutes played, turning Andy Robertson's low ball in before adding a second from close range after being set up by Mohamed Salah half an hour later.
Thiago Alcantara fired in a deflected third to give the Reds a commanding half-time lead before Virgil van Dijk steered a corner home to round off the scoring shortly after the restart.
The victory sees Liverpool keep the pressure up on league leader Chelsea, moving to within a point of the Blues – although the Reds have played an extra game.
Liverpool got off to a flying start as Sadio Mane and Robertson combined on the left before the latter fizzed a low cross into the middle that Jota converted on the stretch.
A couple of chances fell Southampton's way after that, but Liverpool remained the side on top and doubled their lead in the 32nd minute as Salah squared for Jota to tap in his second after playing a neat one-two with Jordan Henderson on the right.
The Reds made it 3-0 just five minutes later as the ball fell to Thiago on the edge of the box and the midfielder advanced into the area before lashing a left-footed strike into the top-left corner via a hefty deflection off the knee of Lyanco.
Van Dijk extended Liverpool's advantage even further in the 52nd minute, volleying Trent Alexander-Arnold's corner under Alex McCarthy, who perhaps should have done better, and in.
Jota spurned a glorious chance to grab his hat-trick, diverting Robertson's cross wide of the target as Jurgen Klopp's men eased their way to the final whistle.
Liverpool's next fixture is a Merseyside derby with Everton at Goodison Park on Thursday (AEDT), while Southampton hosts Leicester City on the same day.