The England midfielder shot under Ben Foster after a clever pass from substitute Gaston Ramirez.
Rickie Lambert and Lallana had shots saved in the first half, before Jay Rodriguez fired wide after the break.
West Brom, with new head coach Pepe Mel in the stands, were denied late on when Artur Boruc saved from Shane Long.
Southampton manager Mauricio Pochettino:
“I think the evolution as of late has been good, I think the team has progressed a lot.
“I think the team as of late has been playing better, but it has been lacking defensive solidity.
“Today we recovered that, we recovered that winning spirit, we recovered that solidity at the back.”
West Brom caretaker manager Keith Downing:
“I think Pepe Mel would have seen us an organised side. Without the ball we restricted Southampton to not many opportunities, not clear-cut opportunities anyway.
“We are all disappointed about what we did with the ball and credit to the opposition, they don’t give you time and quickly press you as soon as they lose it.
“I think he will work on us in terms of possession and creativity, but I thought there was commitment in terms of the team defensively.”
Written by Steve Milne
