Branislav Ivanovic bullet headed home a last gasp winner as Chelsea came rom behind to secure all three points at St Mary's stadium this afternoon.
The Saints went ahead just before the breakthrough Shane Long after the a howler of an error by Baba.
Cesc Fabregas somewhat fortunately equalised with 15 minutes on the clock as Fraser Forster let this cross skip as him. But it was captain marvel Brana who rose above the rest to latch onto a Willian cross to bury the ball into the back of the net.
It was a tentative start by both sides, with possession being turned over quickly without much headway gained.
However Chelsea's Pedro limped off with an apparent hamstring injury after just six minutes.
He was replaced by Oscar.
The home side almost scored three minutes later as Chelsea's rearguard were all at sea and Shane Long inexplicably headed over from six yards out.
But the Blues were themselves unlucky to see Cedic, on his goaline,heading clear an effort from Willian.
But it was the porous defence of Chelsea that was getting the greater inspection and only last gasp clearances from Branislav Ivanovic prevented the home side taking the lead.
After losing control of the ball, Diego Costa decided to discard his face mask on 26 minutes.
Oscar then had the Blues second effort on goal, an Oscar shot, which Fraser Forster dealt with easily.
This was quickly followed by a wayward shot from Costa.
Charlie Austin almost notched up the first goal, on 30 minutes, but his quick turn and shot, on the edge of the Chelsea penalty area just inched wide of Courtois's left upright.
A sustained period of Chelsea possession followed, and while they occupied much of the Saints half, the Londoners failed miserably to pierce the resolute defence of the home side.
Then with three minutes on the clock in the first half, left back Baba made a horrendous and lazy header that fell invitingly to live wire Shane Long, who raced into the Chelsea penalty area and clipped the ball over the advancing Courtois to put them 1-0 up.
Chelsea boss Guus Hiddink hauled off the ineffective Baba any half-time, replacing him with wide man Kenedy.
The first chance of the restart fell to Chelsesa midfielder Mikel but somehow he screwed wide, from six yards a simple header.
Costa then had a tough chance on 59 minutes and could only shank a Eden Hazard right-wing cross overt the Sants' crossbar.
A flurry yellow cards then marred an otherwise sedate and tepid, with Costa the prime architect of the easing of the temperature on the pitch.
It was Costa's never say die running down for a lost cause ball that created the equaliser by Fabregas on 75 minutes.
Costa cut the ball back to in-running midfielder, who, at the edge of the Saints' area clipped in a simple cross, which confused Forster who allowed the ball to slip past him and into the back of his net.
The deserved winner came with a minute to go as Ivanovic rose above the congested six-yard box to seal the three point with a bullet header.
Chelsea
Thibaut Courtois, Branislav Ivanovic, Cesc Fabregas, Baba, Eden Hazard, John Obi Mikel, Pedro, Diego Costa, Willian, Gary Cahill, Cesar Azpilicueta
Subs, Asmir Begovic, Oscar, Bertrand Traore, Kenedy, Loic Remy, Nemanja Matic, Ruben Loftus-Cheek
Saints, Forster, Cedric, Clasie, Fonte, Long, Davis, Romeu, Van Dijk, Betrand, Austin, Targett,
Subs, Stekelenburg, Yoshida, Mane, Tadic, Martina, Ward-Prowse, Pelle
Referee Martin Atkinson