Back in action after the international break, Ronald Koeman’s men had the better of the play at the Hawthorns but struggled to carve out concrete chances.
Jay Rodriguez had the best opportunity of a closely-fought but generally forgettable contest, sending a diving header just wide towards the end of the first half, while both sides had decent-looking penalty appeals turned down.
Despite Saints going into the game on the back of a resounding home win over Norwich a fortnight ago, boss Ronald Koeman opted to make three changes to his starting XI.
Virgil van Dijk – making his debut after joining Saints during the international break – came into defence in place of Maya Yoshida, while Victor Wanyama returned after a two-game absence and Rodriguez was drafted into attack after an impressive substitute showing in that win over the Canaries.
The Baggies, meanwhile, named former Saint Rickie Lambert in their team as well as giving a first appearance to new signing Jonny Evans.
The first chance of the game went Saints way as a minute’s worth of passing and possession eventually lead to Dušan Tadić crossing for Graziano Pellè, but his near-post effort was easily held by West Brom goalkeeper Boaz Myhill.
Saints were given a let-off just after the quarter-hour mark when Callum McManaman tumbled over the sliding Matt Targett in the box as the hosts countered, but referee Stuart Attwell ruled against awarding a penalty.
The Baggies’ first chance came with 26 minutes on the clock as Chris Brunt swung a corner onto the head of Gareth McAuley, but the big defender nodded over the crossbar.
Rodriguez then saw a shot saved after cutting in from the right and then, minute later, had the best chance of the opening half when he headed inches wide from Tadić’s teasing cross.
The second half started quietly but came to life when Darren Fletcher appeared to handle the ball after Wanyama headed down, but Attwell again decided against awarding a spot kick.
Rodriguez then saw a shot held before Salomon Rondon flashed an effort over Maarten Stekelenburg’s goal after sneaking between van Dijk and Targett.
There was a hairy moment for the Saints goalkeeper moments later when he rose to collect the ball after it looped awkwardly off the head of Steven Davis only to spill it, only to gather before the lurking McAuley could make contact.
McManaman then curled a shot wide before a rapid counter-attack by Davis led to Pellè centring for Rodriguez, who could not reach the ball. Tadić quickly took up possession and laid the ball off for James Ward-Prowse, who lashed over.
Koeman made his first substitution shortly afterwards, bringing on Mané – who only returned from international duty late on Thursday evening – for Rodriguez.
Mané had an early chance when Davis headed Myhill’s poor kick into the his path, but the Senegalese’s blistering run forward was not matched by the quality of his finish as he smashed the ball wide.
Pellè then saw a scuffed effort saved as the encounter threatened to peter out, while Mané had an injury-time effort blocked after some neat play on the edge of the Albion box.
The result means Saints are now unbeaten in three league games going into weekend’s clash with Manchester United at St Mary’s.
West Bromwich Albion: Boaz Myhill, Craig Dawson, Gareth McAuley, Jonny Evans (Jonas Olsson 86), Chris Brunt, Callum McManaman (James McClean 61), Claudio Yacob, Craig Gardner, Darren Fletcher (c), Salomon Rondon, Rickie Lambert (Saido Berahino 55). Unused substitutes: Anders Lindegaard (GK), James Chester, James Morrison, Serge Gnabry.
Booking: Brunt (79)
Southampton: Maarten Stekelenburg, Cédric Soares (Maya Yoshida 75), José Fonte (c), Virgil van Dijk, Matt Targett, Victor Wanyama, James Ward-Prowse, Steven Davis, Dušan Tadić, Jay Rodriguez (Sadio Mané 67), Graziano Pellè. Unused substitutes: Kelvin Davis (GK), Shane Long, Oriol Romeu, Juanmi, Steven Caulker.
Referee: Stuart Attwell