Forster was left flattened in the opening minutes of the contest and was replaced by the experienced Kelvin Davis, who produced a number of top saves to prevent Sean Dyche's visitors picking up a second impressive result in a week.
Dyche named the same starting line-up that had triumphed over reigning champions Manchester City last weekend but saw decent chances for Sam Vokes and Danny Ings kept out by the impressive Davis.
His counterpart Ronald Koeman, celebrating his 52nd birthday, saw his side move onto 53 points courtesy of a first-half goal from Shane Long and an unfortunate Jason Shackell own goal - keeping Saints within three points of the Champions League positions.
The game began in an even fashion but was stopped when England international Forster was left in agony and stretchered off after appearing to have his ankle caught by the onrushing Vokes.
Davis came on in his place to make his first appearance in 13 months and he was soon called into action as Burnley steadily continued to grow into the game.
George Boyd found Ashley Barnes whose cross ended up dropping to Vokes - with Davis able to keep out a low drive from the Clarets striker.
The resulting corner fell to Boyd, with Graziano Pelle this time in the way of his shot, before the Scotland international had a strong penalty shout turned down by referee Roger East as Jose Fonte slid in to challenge.
The visitors enjoyed more of the ball but could not create any chances to take advantage of what was turning into a quiet first half for Koeman's side.
The deadlock was broken eight minutes before the interval as Long was on hand to finish from five yards out, turning in Nathaniel Clyne's misplaced effort after Pelle had failed to make contact.
Pelle, without a league goal in 2015, should have doubled Southampton's advantage but could only rattle the crossbar with a close-range volley and he almost paid the price for his miss.
Burnley broke on the counter-attack and Ings got in behind the Saints defence, only to see his curling shot brilliantly kept out by Davis, who was showing no signs of rustiness.
Davis may have been making a difference in the Saints goal but it was nice namesake Steven Davis came close but saw his looping header kept out by a mixture of back-tracking Tom Heaton and the crossbar before Vokes' header on half-time was turned behind by the inspired Davis
Dyche's men were still working hard to get back into the game but Southampton were producing more moments to suggest they could move further clear, Long whistling an arrowed shot just wide with Heaton sprawling to his right.
The second goal did come shortly afterwards as Ryan Bertrand's near-post cross was turned into his own goal by Clarets' skipper Shackell - who could only steer the ball past Heaton with Pelle in close company.
The goal allowed Southampton to take the sting out of the game and Burnley could not force any clear opportunities to reduce the deficit and remain in the bottom three as Saints continue fighting for a top-four finish.
Source : PA