After the hosts had threatened throughout the first half, it was Sadio Mane who opened the scoring in additional time, bending a sublime effort into the top corner from just inside the box to give the Reds the lead.
The visitors furthered their advantage when Roberto Firmino got off the mark for 2019-20 by drilling in a second on 71 minutes; however, former Liverpool forward Danny Ings reduced the arrears when Adrian’s attempted pass ricocheted off him and into the back of the net.
Ings then missed a chance to draw the Saints level before the end in a tense finale, but Jürgen Klopp’s side held on to clinch the three points.