Both sides had cause for optimism going into the clash - Ronald Koeman's men impressing in defeat against Liverpool and Alan Irvine's charges only denied a win by a late Sebastian Larsson goal on the opening weekend.
However, neither side did enough to deserve maximum points on the south coast in a tight affair as Koeman and Irvine continue to await their first top-flight triumph.
Recent signing Shane Long was given a home debut off the bench against his former employers, while West Brom's club-record acquisition Brown Ideye made his bow soon after, but they could not mark the occasion with a goal.
While Dusan Tadic impressed again in his maiden Premier League campaign and Ideye was denied one-on-one by Ben Foster, both sides had to settle for a point.
Just a minute had passed when the visitors saw a penalty appeal waved away - captain Chris Brunt going down in the area - before Victor Anichebe turned his skipper’s cross wide of Foster's goal.
Tadic then crossed for fellow close-season arrival Graziano Pelle who headed Southampton's first attempt wide of goal.
It was Tadic who proved Southampton's main attacking outlet in the first half, while West Brom's lofted deliveries gave Fraser Forster plenty to do in the air on his home debut.
Graham Dorrans failed to cap his surging 28th-minute run with an accurate pass for the in-form Saido Berahino as both sides struggled to find a cutting edge in the attacking third.
A defensive mix-up between Foster and Andre Wisdom almost led to the opening goal of the game as Tadic nipped in to take advantage of confusion in the West Brom defence.
His cross evaded Pelle before Foster made amends for his part in the error by keeping out a low drive from Tadic in the 35th minute.
Koeman introduced former Hawthorns favourite Long at the break and opposite number Irvine brought on Ideye soon after.
The travelling faithful thought the Nigeria international had scored shortly before the hour, only to realise his header had rippled the side netting, with the former Dynamo Kiev later denied at point-blank range by Foster.
Ideye continued to look lively and almost got on the end of Dorrans' throughball a minute from time in a lively finale but ultimately a winning goal proved elusive.
