On the back of Norwich City and Leeds remaining goalless in the first game of the day, the Baggies and Saints served up a far more entertaining spectacle.
However, both goalkeepers held firm at The Hawthorns to keep their respective sides on level terms ahead of Friday's second leg.
West Brom fail to take early lead
During the opening stages, West Brom completely dominated the visitors, yet they were unable to make their territorial advantage count with the final ball lacking.
Southampton slowly grew into the game, forcing West Brom to retreat as they controlled possession, with Flynn Downes seeing a shot well saved by Alex Palmer before Adam Armstrong could only send the rebound into the side-netting.
An overhead kick from Sekou Mara also flew narrowly off target, before West Brom somehow failed to score at the back post, Grady Diangana seeing a header from close range superbly kept out by Saints stopper Alex McCarthy.
Although both sides continued to probe, opportunities began to dry up before the break, perhaps a sign of both teams being wary of falling behind at this point in the tie.
Southampton go on the offensive
At the start of the second half, it was more of the same. Southampton continued their trademark of wanting to keep hold of the ball, but they were struggling to engineer enough space to get a noteworthy shot on target.
However, the best chance of the match went the way of West Brom on the hour mark. Mikey Johnston got to the byline before delivering an inviting cross to the back post where Darnell Furlong sent a volley agonisingly wide of the far post.
Alex Mowatt directed a free kick over the crossbar as the Baggies remained on the front foot, but Martin made a triple change in the hope of stimulating a strong finish from Southampton.
Instead, it was West Brom who almost went in front, McCarthy getting down low to keep out Diangana's shot from 16 yards, before straight down the other end, Ross Stewart's effort was sensationally kept out by Palmer who needed to react to a deflection.
West Brom had a late shout for a penalty deep into six minutes of added-on time as Ryan Fraser appeared to haul down Diangana, but once that appeal was waved away, both teams were left to settle for a share of the spoils ahead of Friday's second leg at St Mary's.