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Fraser Forster was the hero in the dying minutes of the game.
Saints march on, while West Brom falter again.
You can read a full match report here.
Corner to West Brom, Ben Foster is up.
Chris Brunt's flick on is hit by Jonny Evans but his effort is slapped away by Fraser Forster again.
And that's full-time.
What a save.
Jake Livermore plays the ball over the top and Craig Dawson goes with the volley but sees his effort parried away by Fraser Forster.
Five minutes of added time.
Chris Brunt takes it and Fraser Forster is out with the flying fist to clear.
Jordy Clasie is replaced by Harrison Reed.
Five to go here and West Brom win a corner.
Chances coming for West Brom now, but they are just not clear cut enough to trouble the goal.
The Baggies in danger of finishing goalless for the fifth time in their last six games.
Chris Brunt's cross causes chaos in the box and Fraser Forster doesn't connect properly to punch clear, the ball comes to Hal Robson-Kanu but he makes a mess of his shot.
Corner to West Brom.
Can they make hay from a set-piece?
It's their speciality.
No is the answer.
Cedric Soares tackles Nacer Chadli to the ground and goes in the book.
Salomon Rondon's shot is deflected out for a corner.
It's taken quickly by Nacer Chadli but cleared by the Saints defence.
Becoming very open now this.
Nathan Redmond and James Ward-Prowse replaced by Sam McQueen and Josh Sims.
Ben Foster's weak clearance is seized upon by Dusan Tadic, he floats into the box and tries to find the far corner but it's just wide.
Foster breathes a sigh of relief.
Worth mentioning that Darren Fletcher came off for Hal Robson-Kanu.
Nacer Chadli is then set up by Robson-Kanu but shoots at Fraser Forster.
West Brom starting to threaten now.
That would have been a stunning goal.
Nathan Redmond connects first time with Cedric Soares' deep cross at the far post, but his volley is saved by Ben Foster.
James McClean is almost in with his first touch but Fraser Forster just manages to get the ball out from under the Irishman's feet. Crucial stop.
Up the other end Nathan Redmond shoots straight at Ben Foster.
Nacer Chadli floats in a free-kick but that is cleared, the ball comes back to Jake Livermore but he blasts his attempt over.
Matt Phillips is off for James McClean.
Craig Dawson has flattened Shane Long.
No free-kick given.
They both went up for a header and the Irishman came off worse. He receives treatment as he checks his head for some claret.
West Brom on the attack and Chris Brunt sends a cross to the far post for Salomon Rondon but he can only head at Fraser Forster.
Dusan Tadic plays in Shane Long on the right and the Irishman wins a corner.
Tadic takes it but Allan Nyom manages to clear.
Nathan Redmond fires in a low shot but it is saved by the feet of Ben Foster.
Chris Brunt takes a long free-kick but it is headed behind by Salomon Rondon.
Dusan Tadic tries to lash a half-volley over Ben Foster but he doesn't quite get the executiion right.
Early change as Gareth McAuley is replaced by Chris Brunt.
Nathan Redmond is in the area, he tries to do it all himself but is closed down.
Matt Phillips makes his return with a yellow card.
With a lunge on Jordy Clasie, crunching the Dutchman.
Teams as they were in the first-half by the way.
Back under way.
Southampton have bossed possession with 67.5% and they have made 345 passes to West Brom's 162.
Southampton deserve their lead.
They could have had a couple more with Shane Long guilty of missing a few chances.
West Brom's best chance was that Rondon header. A goal every day of the week, were it not for Fraser Forster's hand.
Time for a breather.
Nathan Redmond puts the ball on a plate for Shane Long, who goes for the diving header but nods it wide.
Looking back at replays Shane Long, who had been through on goal, was not touched by Jonny Evans.
Darren Fletcher loses the ball in midfield to Dusan Tadic who plays in Shane Long.
The striker is brought down but the ref plays on.
It breaks for West Brom and Nacer Chadli crosses for Salomon Rondon who rises at the far post but his header is clawed away by Fraser Forster's left hand.
Dusan Tadic takes it but it is a poor attempt and his low shot hits the wall.
Nathan Redmond charges at the West Brom defence in full flight and is stopped by Jonny Evans' knee.
Free-kick to Saints, yellow to Evans.
What a signing he has been.
£10.9m well spent.
Jack Gann: Have been waiting the best part of 2 years for mediocre Clasie to score for so they can use that "clasie finish" line
I didn't disappoint.
Referee Chris Kavanagh, who normally resides in the Football League, is taking charge of his first Premier League game this afternoon at the Hawthorns.
Lovely strike by Jordy Clasie for his first Premier League goal.
Dusan Tadic lays the ball off for the Dutchman, who arrives at the edge of the area and puts his laces through it to drive the ball into the top right corner away from Ben Foster.