Nigel Adkins' side secured only their second victory since Boxing Day to close the gap on leaders West Ham, whose game at Peterborough fell foul of the wintry weather.
Adam Lallana opened the scoring with his ninth goal of the season and Billy Sharp was credited with the second, although Burnley defender Ben Mee got the final touch.
And a deserved win sets up a mouthwatering clash top-of-the-table clash against West Ham at Upton Park on Tuesday night.
Burnley arrived at St Mary's having won five of their last six away games while Saints' recent wobble has seen them without a win in four at home, including Tuesday's FA Cup defeat by Millwall.
But it took the hosts just eight minutes to take the lead when full-back Frazer Richardson overlapped down the right and stood up an inviting cross. Lallana looped in a glancing header at the near post for his second goal in a week.
Three minutes later, with Burnley reeling, former Claret Danny Fox crossed for Rickie Lambert whose shot was fingertipped wide by Lee Grant and from the corner, Lambert's header was cleared off the line by David Edgar.
Sharp, making his full debut since moving to Southampton from Doncaster, got his first sight of goal when he was played in by Jack Cork but his angled effort was deflected wide by Michael Duff.
And in the 33rd minute Saints got the second goal their dominance deserved.
Lambert swung in a cross towards Sharp but as Mee challenged the striker the ball cannoned off his knee, bounced past Grant and into his own net.
Burnley manager Eddie Howe made a double substitution at the break, throwing Josh McQuoid and Marvin Bartley into the action.
But Saints were still in control and could, and probably should, have added to their tally in the second half.
Cork's superb pass sent Lambert charging towards the Burnley area and his cross just eluded substitute David Connolly.
Grant also kept out Lallana's close-range shot before Connolly thought he had snaffled a third after the Burnley goalkeeper spilled a long-range effort from Lambert, but an offside flag curtailed his celebrations.
Nevertheless, Southampton were rarely troubled as they registered a first home win of 2012 as well as the perfect preparation for Tuesday's trip to east London.