Goals from Adam Lallana and Billy Sharp gave Nigel Adkins' side only their second victory since Boxing Day and moved the second placed Saints within one point of leaders West Ham, whose game at Peterborough was postponed due to a frozen pitch.
Southampton had gone without a win in their last four home matches, including an FA Cup exit against Millwall in midweek, but Lallana opened the scoring in the eighth minute with his ninth goal of the season.
Billy Sharp, a recent signing from Doncaster, got the second goal in the 33rd minute via a deflection off Burnley defender Ben Mee.
That was enough to seal the points and set up a crucial clash top-of-the-table clash against West Ham at Upton Park on Tuesday.
League Cup finalists Cardiff saw their promotion challenge falter at the King Power Stadium as Leicester's Paul Gallagher scored twice for the hosts.
Malky Mackay's team, who face Liverpool at Wembley later this month, suffered back-to-back league defeats for the first time this season as they followed up last week's 3-1 defeat at home to Blackpool with another poor display.
Gallagher opened the scoring with a penalty four minutes before half-time and the former Blackburn forward struck again with a superb 71st minute free-kick before Peter Whittingham reduced the arrears from the spot six minutes later.
Leicester move to within six points of the play-offs, while Cardiff remain fourth but slip five points behind second-placed Southampton.
Hull climbed up to fifth place with a 3-0 home win over Bristol City thanks to goals from Jack Hobbs, Robert Koren and Matty Fryatt.
Reading are one place outside the play-offs after Jimmy Kebe and Jason Roberts scored in a 2-0 win over bottom of the table Coventry at the Madejski Stadium.
Kebe opened the scoring with a deflected strike in the 25th minute before former Blackburn forward Roberts bundled the ball home from Ian Harte's corner two minutes before the break.
Alan Navarro scored in stoppage time as Brighton snatched a 2-1 win at managerless Leeds.
Luciano Becchio cancelled out Brighton striker Craig Mackail-Smith's opener but Navarro's low drive from the edge of the box went in via a deflection off Adam Smith to silence Elland Road.
Elsewhere, Millwall drew 0-0 with Derby, Nottingham Forest were held to a 1-1 draw by Watford and Ipswich's home match against Middlesbrough was abandoned due to the poor state of the frozen pitch.
Source: AFP
Source: AFP