Gareth Bale came closest to breaking the deadlock with a 25-yard free-kick that rebounded off the post.
Bale's left-foot strike left Baggies keeper Pascal Zuberbuhler stranded, but he was saved by the base of the left-hand post and the ball was cleared upfield.
The free-kick was given after Curtis Davies fouled Grzegorz Rasiak just outside the box.
John Hartson and Bradley Wright-Phillips both had good chances to score in the first half but could not take their opportunities.
Southampton pressed hard during the second half, but could not create enough clear chances to be able to win the game.
Hartson had a fabulous chance to break the deadlock after just two minutes but he could only put his header where Kelvin Davis in the Southampton goal could reach it.
Hartson, the Wales international striker, held his head in his hands as he realised that he should have scored.
Wright-Phillips linked up with Rudi Skacel and Rasiak to head back into the area for Southampton in the sixth minute, but the move ended with Wright-Phillips' overhead kick going over the bar.
Referee Steve Tanner gave the first yellow card of the game to Hartson after he left his foot up in a challenge with Alexander Ostlund that left the Swedish right-back crumpled on the floor.
Southampton were pressing hard at this point and from Bale's cross Rasiak's weak header was saved easily by Zuberbuhler.
On 38 minutes Rasiak played Wright-Phillips through, but his fierce drive was turned round the post by Zuberbuhler. Zoltan Gera hit back for West Brom with a right-foot shot that went narrowly wide of the post.
Southampton came out firing after half-time and put constant pressure on the West Brom goal, Wright-Phillips played in Rasiak whose shot was saved easily.
John Viafara and Djamel Belmadi also both came close to opening the scoring, but could not take their opportunities.
From a Saints corner Chris Baird had a golden chance to open the scoring, but he sliced his left-foot shot well wide of the left-hand upright.
After Bale's free-kick came close, Southampton put constant pressure on the West Brom goal, but without creating any real opportunities.
It was West Brom who came closest in the closing stages to breaking the deadlock. Gera tried an ambitious overhead kick from substitute Darren Carter's cross, but Davis managed to save the shot and clung on to the loose ball from the rebound.