
Adam Armstrong has scored 11 goals this season
Adam Armstrong scored twice to lift Southampton to within a point of the Championship play-offs and add to the pressure on West Brom boss Ryan Mason.
Leo Scienza claimed the opener for Saints before Armstrong's first-half double made it seven goals in six games for the striker.
West Brom rallied in the second half and Karlan Grant and Nat Phillips scored to set up a frantic finale before the Baggies sank to their seventh successive away defeat.
Tonda Eckert has now won six of his seven games in charge since replacing Will Still and is steering Southampton quickly up the table.
The south coast club have found the target 21 times under Eckert after managing just 13 in their 13 league games with Still at the helm.
With the Baggies down in 16th after just two wins from their past 10 games, fresh questions are likely to be asked of progress under Mason who was appointed in the summer.
West Brom academy graduate Tom Fellows showed the Baggies just what they are missing since his £10m summer switch to Southampton as he created the opening goal.
Fellows turned and ran three quarters of the pitch before finding Scienza on his right, who scored expertly into the far corner.
As fluent as Southampton were, West Brom didn't help themselves and they gifted Saints a second when Callum Styles played the ball back to Phillips, who was robbed by Armstrong to score his first of the night.
West Brom goalkeeper Joe Wildsmith then gave the ball away for Caspar Jander to shoot over before Saints grabbed their third after some intense pressing.
Taylor Harwood-Bellis pounced on an errant pass and found Finn Azaz, who fed Armstrong to score with a neat finish across goal into the far corner.
West Brom turned the game on its head in the second half and Grant scored his first goal of the season with a left-footed effort.
The Baggies rallied and Isaac Price had a couple of efforts before Phillips headed home from close range four minutes from time to set up a grandstand finish.
Samuel Iling-Junior came close to an equaliser only to shoot wide in stoppage time.
'It showed what energy St Mary's can create for us' - reaction
Southampton boss Tonda Eckert told BBC Radio Solent: "I think the second half showed what an energy St Mary's can create for us and I take that as a positive.
"I'm trying to look at the result more positive as it's the Championship and there are no easy games.
"Both goals came from dead-ball situations and we need to defend them better, but we won the game and take three points.
"The first half was excellent and we came out strong. In the second half the game became more difficult when they scored and we just had to bring the game over the line, which we did."
Tonda Eckert: 'The fans were there for us'
West Brom manager Ryan Mason told BBC Radio WM: "No, it's certainly not the time to do that [launch a comeback] when you're 3-0 down after the first half and the nature of why we were 3-0 down.
"I think the bigger concern, yes, in the second half, how that panned out. But football isn't 45 minutes. It's 90 minutes and we were not good enough in that first half, certainly.
"They are many different things. Obviously, we've made individual errors. Having the bravery and the belief to execute something, I don't think we quite had that in the first half.
"Did we have it in the second half? Yes, we did, but at this level, and at any level, to come back from three goals down is extremely difficult."
Mason: 'Not good enough in the first half, certainly'
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