The Baggies welcomed Ralph Hassenhuttl’s side to The Hawthorns having put five past Chelsea in their previous outing.
And they should have scored as many against the Saints following a rampant first-half display that saw them create a host of clear-cut chances.
In the end they had to settle for just the three goals, with Matheus Pereira, Matt Phillips and Callum Robinson the men on target.
But it could easily have been more with Mbaye Diagne hugely unfortunate to see a goal ruled out by VAR when the cameras were unable to determined whether his upper body was onside or offside.
Thankfully it didn’t matter with the Baggies going onto register their biggest home win in the top flight since November 2016.
The result means they now sit eight points from safety in the Premier League with seven games remaining.
Boss Sam Allardyce admitted during his pre-Southampton press conference that he was going to make a late call on what team and formation to deploy against the Saints.
The Baggies impressed in a 3-5-2 system during the opening stages of their win at Chelsea.
But they became more dangerous when Robinson came off the bench and they switched to a 4-2-3-1.
And it was that system Allardyce plumped for here with Robinson earning a recall to the starting XI following his two-goal heroics at Stamford Bridge.
The Republic of Ireland international started on the left wing with Phillips on the right and Pereira in the number 10 role.
Diagne was the lone striker with Okay Yokuslu partnering Ainsley Maitland-Niles in the middle of the park.
The switch to a back four meant Semi Ajayi had to make do with a place on the bench where he was joined by Conor Gallagher who couldn't feature against Chelsea under the terms of his loan.
Southampton lined up in a 4-4-2 formation that is often referred to as a 4-2-2-2 because of how narrow Hasenhuttl likes his team to play.
Danny Ings was partnered by Nathan Redmond up front with Stuart Armstrong and Theo Walcott the widemen.
In what proved to be a remarkable first-half, the game's first big talking point arrived just four minutes in - with Albion again seeing a goal controversially ruled out by VAR.
After Phillips had seen a shot beaten away by Fraser Forster, Darnell Furlong powered a strike towards goal which Diagne nodded in from close range.
Immediately the linesman flagged for offside.
But VAR decided to have a look with it then emerging the call was so close there wasn't a camera angle that could definitely confirm whether or not Diagne's upper body was onside or offside.
And because it couldn't be determined one way or another, the goal was ruled out with VAR deciding to stick with the original on-field decision.
If Albion's players felt that decision was an injustice, they didn't show it with Allardyce's men going to play some sensational football from that point.
Maitland-Niles found Phillips in the box but his powerful strike deflected over.
A brilliant through-ball from Pereira then send Diagne clean through on goal with only the keeper to beat.
But the Senegal international got his timings all wrong and sliced a strike high wide when he really should have scored.
In a match that was now like a game of basketball, Southampton began to grow in stature.
Stuart Armstrong saw a strike from 20-yards parried away by Johnstone.
Then from the corner, a big ricochet could have seen the ball go anywhere but instead it landed in the arms of the England international.
Albion, though, were playing with real intensity and aggression.
And they finally got the lead they deserved on the half-hour when Forster hacked down Pereira for a stonewall penalty.
The Brazilian then dusted himself down to calmly score from the spot.
Just three minutes later Albion had doubled their advantage with Diagne going someway to atone for his earlier miss.
After first doing well to read and intercept a loose pass, the striker then charged at goal before delivering the most wonderfully inviting cross.
And that was smashed into the net from close range by Phillips.
Those goals meant Albion made their way off at the break having scored seven goals in their last 90 minutes of football - with all five of their strikes at Stamford Bridge coming in the 45th minute or later.
The only downside was that they weren't further ahead with Allardyce's side dominant right from the off.
It was Southampton who created the first chance following the re-start with the dangerous Kyle Walker-Peters flashing a shot right across the face of goal.
Saints were much brighter following the re-start with Albion guilty of sitting a bit too deep.
And they threatened again on the hour when Armstrong hit a fierce effort from 20-yards which Johnstone gathered expertly.
The Baggies had been facing relentless Southampton pressure but Kyle Bartley and Furlong, in particular, were producing some outstanding defensive displays.
And that gave them the platform to wrap the game up in the 69th minute when Yokuslu’s through-ball sent Robinson charging towards goal.
The Republic of Ireland international still had a lot to do and did well to hold off Jannik Vestergaard.
And he then emphatically fired past Forster for his third goal in two games.
Allardyce made his first change just moments later with Conor Gallagher replacing Robinson. Diagne then made way for Hal Robson-Kanu.
Gallagher’s introduction allowed Albion to shift to a 4-3-3 formation to help shore things up.
And they looked to have seen out the game comfortably from that point until Southampton were awarded a penalty in stoppage time.
The spot-kick was given after Conor Townsend fouled Moussa Djenpo in the box.
But England international James Ward-Prowse saw his strike brilliantly saved by Sam Johnstone to perfectly round-off an emphatic and complete performance from the Baggies.
Albion (4-2-3-1): Johnstone, Furlong, Bartley (Ajayi 85), O'Shea, Townsend, Yokuslu, Maitland-Niles, Phillips, Pereira, Robinson (Gallagher 72), Diagne (Robson-Kanu 76).
Subs not used: Button, Gibbs, Peltier, Livermore, Diangana, Grant.
Southampton (4-4-2): Forster, Walker-Peters (Djenepo 87), Vestergaard, Bednarek, Bertrand, Redmond, Ward-Prowse, Diallo, Armstrong, Walcott (Adams 76), Ings (Tella 87).
Subs not used: McCarthy, Stephens, Minamino, Salisu, Ferry, Jankewitz.