Morgan Schneiderlin neatly converted a Jay Rodriguez knock-down in the sixth minute to put Southampton ahead at St Mary’s, before Rickie Lambert doubled the hosts’ lead with a deflected free-kick.
Philippe Coutinho replied for Liverpool on the stroke of half-time, but Rodriguez made sure of victory in the 80th minute as Mauricio Pochettino's side pulled seven points clear of the relegation places.
Meanwhile, Arsenal won 2-0 at Swansea City to move to within two points of fourth-place Chelsea. January signing Nacho Monreal and Gervinho struck late in the game at the Liberty Stadium as Arsene Wenger’s side responded in positive fashion to their mid-week elimination from the Champions League.
SRK-Gauri anniversary: B-Town stars and their non-filmi better halves
Birthday special: Popular mothers and daughters in Bollywood
Spotted: 'Kaabil' star Hrithik Roshan with dad Rakesh Roshan
'Rock On 2' trailer launch: Farhan, Shraddha enthrall audience with live gig
Photos: Deepika Padukone, Sushmita Sen with daughters at Mumbai airport