Saido Berahino’s goal after 72 seconds was enough for a resurgent West Brom, who are now in 13th place in the Premier League, to secure victory at the Hawthorns.
Since Pulis took over on January 1, West Brom have lost just one of their eight games in the Premier League, taking 13 points along the way while keeping five clean sheets.
The job mirrors the work Pulis did at Crystal Palace last season when he saved the Eagles from relegation, finishing the season in 11th place after they were in the drop zone at Christmas.
???I haven???t done anything yet,??? said Pulis.
???We???ve got 30 points. I think 40 points will be good for safety this year, so we have to keep going. There???s more games to be played. The problem is that people take their foot off the gas and this game is relentless.
“If you do that then you get a kick up the backside. We???ve got a massive game at Aston Villa on Tuesday and we???ve got to approach it in the right manner.???
Berahino???s goal was a stunning finish and capped an impressive display by the striker, who Pulis revealed played with a pain-killing injection after suffering a knock against Sunderland last weekend.
He lasted 55 minutes against Southampton before being replaced by Youssouf Mulumbu, while striker Brown Ideye also had to be substituted late on with an injury.
Pulis praised both players for playing through the pain barrier.??
He said: ???They both carried knocks into the game. It just shows they???ve got a good spirit in the dressing room now. A good togetherness and people want to play.
“Saido had an injection before the game to play. He should have an injection every game ??? scoring goals like that! I???ll be mentioning that to the doctor.???