A James Beattie penalty and a John Arne Riise own goal earned the Saints a fifth win in seven games as Liverpool, without the injured Michael Owen, looked toothless.
Riise's error - a pinpoint header into his own net within minutes of coming on - suggested that the success of Gordon Strachan's 13th game in charge of Southampton owed more to luck than judgement.
But, putting aside's Liverpool's dismal form, the home side were definitely worth their win. With no Owen, the visitor's striking onus fell on Jari Litmanen and Nicolas Anelka. The duo warmed to their task slowly but did produce the moment of the first half on 36 minutes.
Litmanen headed to the on-loan Paris St Germain forward but Anelka's strong, dipping first-time shot was acrobatically palmed away by Jones at his near post.
For the most part, the half was hurried and lacked precision. Paul Williams nicked the ball from Anelka as he was poised to shoot and Claus Lundekvam produced a timely block to keep out Danny Murphy's eight-yard shot.
Saints, who lost Rory Delap to a calf strain after 33 minutes, looked lively when they got the ball out wide. Wayne Bridge tested Jerzy Dudek with two crosses and Marian Pahars linked well with James Beattie, but was closed out.
At the other end, Jason Dodd deflected Litmanen's 18-yard drive over the crossbar.
Saints started to come into their own after the interval. Dudek was forced to parry a Marsden shot at point-blank range before Sami Hyppia chopped down Matt Oakley to concede a penalty.
Beattie calmly put the ball to the left of Dudek to register his ninth Premiership goal of the season.
Liverpool countered but Murphy's close-range volley was bravely blocked by Dodd. Moments later Riise amazingly headed a Pahars centre into his own net to seal Liverpool's fate.