A contest lacking in cut and thrust produced few opportunities of note, with Dusan Tadic coming as close as anyone in the opening 45 minutes as his prodded effort produced a smart low stop from Ben Foster.
Changes after the interval improved things slightly, with big-money signing Brown Ideye handed his Premier League bow by West Brom and showed glimpses of what he might be capable of when up to full speed – with one close-range effort well blocked by Fraser Forster.
James Ward-Prowse also clipped the outside of the post with a dipping free-kick, but there was to be no breakthrough and the points were shared.
The game proved to be a missed opportunity for new Southampton manager Ronald Koeman and his summer recruits to show Saints fans they are moving on from a summer of upheaval.
Having impressed for large parts of their opening defeat at Liverpool, Koeman warned other clubs would have taken note of how good his side are.
But it was the visitors who started well at St Mary's, with Alan Irvine's charges also looking to make an impact.
Baggies' captain Chris Brunt had a shout for a penalty as early as the second minute, but referee Roger East was unmoved as he fell inside the area while looking to turn the Southampton defence.
Brunt was involved again shortly afterwards as his cross was met by Victor Anichebe, who reacted quickest to swing a boot at the ball, only to see his effort fly wide.
With former West Brom striker Shane Long again only starting from the bench for Koeman's side, fellow summer signing Pelle was given the responsibility of operating as the main forward.
The former Italy Under-21 international had Southampton's first chance of the game, but could only glance an eighth-minute header wide of a post.
But again it was the travelling fans who saw their side come close to breaking the deadlock as Graeme Dorrans had his low shot bravely blocked by Saints captain Jose Fonte.
Southampton started to turn the tide in their favour and it was Jonas Olsson who had to block Pelle's effort after good work down the left by Ryan Bertrand.
Pelle was again involved as Tadic's cross drifted just too high for the ex-Feyenoord man to reach, with West Brom goalkeeper Ben Foster caught in no-man's land after a mix-up with Andre Wisdom.
England international Foster was on hand to make the first real save of the game as he pushed away Tadic's close-range effort after the Serbia international had done well to initially win the ball back.
Long was introduced at the break in place of Steven Davis, with Ideye brought on for his Baggies debut 10 minutes later.
But it was Tadic who wasted the best chance in the early stages of the second half, drifting inside unchallenged before rolling a tame shot at Foster.
West Brom hit their hosts on the break and Sebastien Pocognoli's deep cross was headed into the side-netting by Ideye.
That proved to be Pocognoli's last contribution as the Belgium international was forced off, with Jason Davidson, another debutant, taking his place.
Tadic was proving to be the man most likely to make something happen and he came close to his first Saints goal after drilling Long's knock-down narrowly wide.
With Southampton starting to ask more questions, James Ward-Prowse hit the outside of a post with a bending free-kick, with Foster seemingly well-beaten.
Irvine's side were dangerous when they went forward and Ideye continued to impress as he turned Fonte inside the box and forced the best save of the match out of a sprawling Forster.
But neither side could fashion a chance to take all three points with a late winner, with a point apiece a fair reflection of a forgettable afternoon.
Phil Thompson on Southampton v West Brom
Both sides were giving the ball away, but you were looking at Southampton, as the home team, to make all the play. With Pelle being up front they’ve got no pace whatsoever with nobody running in behind. That means that if you can’t keep the ball to build up, you’ve got a problem.
This is a game where West Brom are probably happy with a draw, but until Ideye came on they had no real cutting edge. Everybody put a shift in, but everybody – even Roger East the referee – had an easy game. It was that sort of an afternoon.