Rickie Lambert followed up a goal on his England debut in midweek by scoring a last-minute winner from the penalty spot for Southampton.
A disappointing game was heading for a goalless draw when West Brom's Youssouf Mulumbu brought down Luke Shaw.
Southampton striker Jay Rodriguez had earlier hit the crossbar in a match of few clear-cut chances at The Hawthorns.
West Brom's best opportunity came when Graham Dorrans sent a 25-yard free-kick narrowly over the crossbar.
The dramatic finish was in sharp contrast to a scrappy encounter as West Brom struggled to get going despite the presence of new striker Nicolas Anelka.
Representing his sixth English club and making his first Premier League start for two years, the 34-year-old former France international endured a frustrating debut and was substituted seven minutes from time.
Although West Brom finished eighth in the Premier League last season, they have now won just one of their last 10 league games.
Southampton included four Academy graduates in the starting line-up, while defender Dejan Lovren impressed on debut following an £8.5m move from Lyon.
The Saints were sharp and lively as 18-year-olds Jamie Ward-Prowse and Shaw caught the eye throughout.
Ward-Prowse stung the palms of West Brom goalkeeper Ben Foster from distance in the 20th minute, a rare moment of entertainment in a game that was a poor advert for the top flight.
Southampton captain Adam Lallana found the net from close range in the 33rd minute but it was ruled out for offside, before former Burnley striker Rodriguez struck the woodwork shortly after half-time.
A draw was looming before Mulumbu stuck out a leg and sent Shaw tumbling.
Lambert, who scored the winner against Scotland with his first touch in an England shirt on Wednesday, drilled the spot-kick past Foster to cap a wonderful week.
West Brom manager Steve Clarke:
"I think it was (a harsh) result. We struggled to get into it in the first half but I think we had better control after the interval.
"The fans will be disappointed with me and the team.
"I'll think about that (making new signings) more on Sunday. Today is all about disappointment."
On the decision to award a penalty:
"I've seen it. There's no doubt in my mind, it's a very soft decision."
Southampton manager Mauricio Pochettino:
"We actually scored a goal before (the penalty) that wasn't allowed to stand and that was a legitimate goal.
"But I think in the overall reading of the game, we were superior to West Brom.
"You always have to believe you are going to win, through to the last whistle, and because of that I want to congratulate my team.
"Even in the second half, when West Brom were pressing us quite hard, my team showed the resolve to keep it at 0-0 and we were able to get that winning goal in the end."