Albion lead at St Mary’s after Glenn Murray smashed home a 14th minute penalty.
Wesley Hoedt brought down Solly March and Murray notched his ninth of the season
Southampton’s best chance came after an error from Maty Ryan as the Aussie keeper cleared the ball.
Pierre Emile Hojbjerg charged him down but his effort smashed against the bar and was booted away by Lewis Dunk.
Leo Ulloa is on the bench for the Albion.
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