The Blades took a deserved lead when Keith Gillespie latched onto Paddy Kenny's clearance and fired home.
James Beattie then volleyed wide before Saints equalised, Nathan Dyer picking out Grzegorz Rasiak to steer in.
Saints' winner came when Kenny flapped at Andrew Surman's free-kick and John Viafara poked home, as they won for the first time in four games.
Southampton boss George Burley "We had to work hard for the win but I don't remember Kelvin Davis having a serious save to make.
"it is not always about playing silky football - they put us under pressure in the second half but we played well as a unit.
"It is a great win for us after those two home games - you don't always get what you deserve in football but I am pleased with the way we responded at Bramall Lane."
Sheff Utd: Kenny, Geary, Morgan, Cahill, Naysmith (Armstrong 63), Gillespie (Shelton 71), Hendrie (Tonge 63), Montgomery, Stephen Quinn, Stead, Beattie.
Subs Not Used: Lucketti, Sharp.
Booked: Beattie.
Goals: Gillespie 12.
Southampton: Davis, Ostlund, Dailly, Thomas, Ifil, Wright-Phillips (Saganowski 65), Dyer, Viafara, Surman (Euell 78), Rasiak, Safri.
Subs Not Used: Bialkowski, Wright, John.
Booked: Thomas, Viafara, Ostlund, Dyer.
Goals: Rasiak 19, Viafara 31.
Att: 24,561.
Ref: Tony Bates (Staffordshire).
E-mail this to a friend 
Printable version 
Bookmark with:
What are these?