This result marked the first time since May 2018 that the Baggies have recorded back to back victories after their impressive win 5-2 win at Chelsea last time out, and it moves them eight points adrift of the relegation zone with seven games remaining.
In truth, it was entirely what Sam Allardyce's deserved and after having a controversial goal disallowed early on, added with the fact that they squandered a host of opportunities, it could have ended up being a far more embarrassing end for Southampton.
Story of the game
The Baggies started the game the brighter and thought they had broken the deadlock inside a couple of minutes when Mbaye Diagne headed home from close range after getting on to the end of a Pereira volley.
However, the linesman's flag was raised for offside and after a lengthy check from VAR, the goal was ruled out even though Kyle Bartley appeared to be the one in an offside position, instead of the actual goalscorer
With the hosts dominating the early stages just before the tenth-minute mark, Kyle Walker-Peters did excellently to get free down the right-hand side, but instead of finding a man in the middle, he opted to shoot straight at Johnstone.
From the following corner, the ball fell to Theo Walcott on the edge of the box, but his first-time volley was sliced wide of the mark.
These opportunities failed to halt West Brom's progress though as just before the quarter of an hour mark, after good build-up play, a Matt Phillips cross from the right was deflected narrowly over the crossbar.
A couple of moments later Darnell Furlong had a huge chance to give his side the lead, but his flicked header inside the area flashed past the left-hand post.
Allardyce's outfit kept on coming as five minutes later, Robinson latched on to a Bartley header inside the area, but his effort was straight at Fraser Forster.
Despite the dominance of the Baggies, Danny Ings may have felt he should have done better on the 25th-minute mark when his smart feet found him room inside the area, but his curling effort drifted a couple of yards wide of the right-hand post.
Then a minute later, the English forward had another chance when he was found at the back post by a Stuart Armstrong scuffed shot, but his low strike from a tight angle went all the across the face of goal.
After a short decent spell by the Saints, West Brom created yet another chance on the 28th-minute mark and this one should have been taken, as after some quick play by the hosts, Diagne was found in on goal but his effort curled away from the right-hand post.
Then in this end to end encounter, Ralph Hassenhuttl's side went up the other end and were denied from grabbing the opener themselves through a fine Johnstone stop, who did well to turn behind Armstong's drive from range.
A few minutes later after a host of chances, West Brom were awarded a spot-kick when Robinson was found unmarked inside the area, and after getting to the ball ahead of Forster, he tumbled over with the referee having no hesitation to award the penalty.
Pereira stepped up and had no problem smashing the ball down the middle to hand the hosts a valuable lead.
Then four minutes later, things got even better for Allardyce's side as they doubled their advantage after Diagne intervened from a loose Southampton pass.
He then spotted the run of Phillips at the back post, and his low cross found the winger who had the simple task of stroking the ball into the roof of the net.
After the interval, as expected Southampton began to pile on the pressure with Walker-Peters having a sight of goal inside 51 minutes, but his low drive arrowed just wide of the left-hand post.
The visitors were really starting to gain a grasp on the game and achieved their first shot on target of the half just after the hour mark, but Armstrong's strike from range was comfortably held by Johnstone.
Moments later, Hassenhuttl's team had a big claim for a penalty when Nathan Redmond thought he felt a touch inside the penalty area but the appeals were instantly dismissed by Simon Hooper.
Six minutes later, West Brom had their first chance of the second period to test out Forster through a free-kick, but Okay Yokuslu's effort sailed wide of the woodwork.
Then even though it was Southampton that looked the more likely to halve the deficit, Robinson wrapped up the three points for the hosts when he smashed the ball home after being slipped in on goal by a well-weighted pass by Yokuslu.
With a humiliating defeat looming for Hassenhuttl, Redmond tried to repair some of the damage that had been done, but his long-range drive with 15 minutes to go sailed narrowly over Johnstone's crossbar.
Five minutes later, the Saints caught the hosts on the counter-attack, but substitute Che Adams ultimately chose the wrong option as his shot from a tight angle flashed wide of the far post.
Then in stoppage time, Southampton had a chance to claim a consolation goal when Moussa Djenepo was brought down in the box by Conor Townsend.
Although, Johnstone stood tall and did brilliantly to get across to James Ward Prowse's penalty kick to ensure that his side maintained a clean sheet, but more importantly it helped wrap up a vital three points for West Brom.
Platform to build on going into tough end of season run in
There is no doubt that Allardyce will be keen to use this result and performance as a model and example going into the final stages of the season.
Despite it being a clear important three points, there is still a lot of work to be done and with the Baggies still having to play the likes of Leicester City, West Ham and Liverpool, it still remains hard to see if they have enough in them achieve a great escape.
Saying that this is something that could be used to Allardyce's advantage as with their chances of staying up being slim going into those last seven games it means that they have the chance to play free-flowing football.
This is due to the pressure being off them considering that they are expected to make the drop back to the Championship.
Many things to learn from going forward from saints first-half showing
Despite the fact that credit must be given for West Brom's formidable first-half performance, blame must also be put out to Southampton who time and time again just gave the hosts space in dangerous areas which consequently allowed them to cut open the Saints backline.
This is something that will have hugely disappointed Hassenhuttl as it was ultimately the primary reason to why they lost to such a heavy margin.
The worst thing about this is that there were early signs of West Brom getting far too much room in behind the Southampton defence, just for 45 minutes they did not appear to drop back deeper to deal with the problem.
After the break, the West Brom onslaught did stop as Southampton did considerably improve in the second half but really by then it was too late as the visitors really struggled to muster too many clear cut opportunities.
When reviewing the game, this is something that Hassenhuttl must learn from and make it clear to his players to cut out, especially with an important FA Cup Semi-Final against Leicester at Wembley on the horizon.
Star Player- Callum Robinson
The forward who was recalled to the starting lineup after his brace last time out at Stamford Bridge was relentless for 90 minutes and throughout the 90 minutes caused Southampton plenty of problems.
He was a threat down the left-hand side as off the ball he was always looking to make runs that the Saints backline had to be cautious of.
Then when on the ball he was always looking forward and striving for ways to find space in behind Southampton's line of defence.
Not only this, but he further took his goal really well as he had to have the composure to find a way past Forster and for the penalty he was clever in his ways to force the goalkeeper to bring him down.
Over the past few games he has really provided Allardyce with a reason to give him minutes on to the football pitch and this is something that he will be hoping to continue to do from now until the end of the campaign.