Three second half goals from Fernando Torres, Willian and Oscar secured the points for the visitors.
Southampton could have gone ahead had it not been for some last-ditch tackling from Ashley Cole, John Terry and Gary Cahill. But their finishing let them down.
Talk of Saints pushing for a surprise European spot has diminished following their recent poor form, but Mauricio Pochettino is not a worried man.
"Rome wasn't built in a day," the Southampton manager said.
"We have been facing some of the top sides and that has been tough.
"We are a young side and we are still learning. We have to keep on believing on our style of play."
Southampton face West Brom in the Premier League on the 11th January.