Saints were in control after Marian Pahars' close-range header and Nigel Quashie's brace, including one penalty, which put them 3-0 up at the break.
But the introduction of David Healy with 20 minutes remaining sparked an incredible turnaround by the visitors.
First Paul Butler headed in then Robbie Blake tapped home before Healy's chip was handled and he popped in a penalty. Liam Miller side-footed in the winner.
Leeds boss Kevin Blackwell: "All the plaudits go to the players. That's something you see only rarely in football, and we're on the right end of it.
"At half-time I told them firstly to go out and regain some pride, and then see if you can get a goal, to see how that affects Southampton.
"That team has got us in the top six, so deserved the chance to dig us out."
Southampton: Niemi, Delap, Lundekvam (Hajto 45), Svensson, Higginbotham, Oakley, Wise (Fuller 45), Quashie, Pahars (McCann 45), Walcott, Ormerod. Subs Not Used: Belmadi, Smith.
Booked: Wise, Quashie.
Goals: Pahars 27, Quashie 35, 45 pen.
Leeds: Sullivan, Kelly, Butler, Kilgallon, Harding, Richardson (Healy 67), Derry, Miller, Lewis, Hulse, Blake. Subs Not Used: Pugh, Bennett, Walton, Douglas.
Booked: Butler, Lewis.
Goals: Butler 71, Blake 77, Healy 84 pen, Miller 86.
Ref: I Williamson (Berkshire).