The full-back (pictured above) slotted past substitute goalkeeper Bradley House after Alex Palmer had been sent off for bringing down Jonathan Afolabi in the area.
Belgium international midfielder Nacer Chadli made his comeback from injury for the hosts before going off at half-time.
Saints are up to fifth after their second win in succession, while West Brom are behind Fulham on goal difference at the bottom.
Both teams are next in Premier League Cup action on Friday 29 September. West Brom visit Aston Villa, while Southampton entertain Watford.