Blackburn Rovers recorded back-to-back wins and moved up to second place with a 3-1 win at Arsenal.
Marc Overmars gave the Gunners a half-time lead but Blackburn came out fighting after the interval and Jason Wilcox levelled for the visitors, while goals from Kevin Gallacher and Tim Sherwood wrapped up the victory.
The result took Blackburn to 36 points, four points behind leaders Manchester United, while Arsenal dropped to fifth on 30 points, a point outside the top four.
Southampton leapfrogged Liverpool in the table as Gordon Strachan's side triumphed at Anfield.
Brett Ormerod opened the scoring in the second minute, his third goal in two matches, and Michael Svensson added a second with a header on 64 minutes.
Emile Heskey gave Liverpool hope with a scrambled effort, but Gerard Houllier's side were unable to get an equaliser and slipped to a fourth home league defeat of the season.
The result left Liverpool ninth on 22 points, three points behind fourth-placed Fulham, while Southampton moved up to sixth on 23 points.