Goals from Grzegorz Rasiak and Rudi Skacel gave Southampton their first Championship away win since September.
Saints took the lead just before the half-hour mark, Gareth Bale whipped in a cross which Surman flicked on for Rasiak to loop over Graham Stack.
Skacel doubled the advantage when he was allowed an age in which to lash his finish past Stack.
Five minutes later, Rasiak headed home from a corner almost completely unchallenged to seal the victory.
Leeds boss Dennis Wise on missed chances and signing players:
"I think if we had got back into the game when it was 1-0, or if they had gone 1-0 down, it is going to be a totally different game."
"I will bring players in and players will go. It's best to keep it at that."
Southampton manager George Burley:
"I feel we've played well and not got the results we deserve. We have showed what we're capable of.
"Our problem this season has been that we have dominated so many games, had so many shots - more than anybody in the Championship - and not taken them.
"If you start with an attitude away from home that you're going to try to win, you always have a good chance."
Leeds: Stack, Foxe, Heath, Kilgallon, Crainey, Blake, Derry, Douglas, Lewis (Beckford 70), Horsfield (Moore 55), Healy.
Subs Not Used: Warner, Westlake, Johnson.
Southampton: Davis, Makin, Baird, Lundekvam, Bale, Skacel, Wright, Pele, Surman, Wright-Phillips (Viafara 64), Rasiak (McGoldrick 81).
Subs Not Used: Bialkowski, Ostlund, Licka.
Booked: Wright-Phillips.
Goals: Rasiak 29, Skacel 69, Rasiak 75.
Att: 19,647
Ref: S Mathieson (Cheshire).