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.
West Brom 0-1 Southampton: Pochettino praises Lambert after 'dream week'
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.
This was only Southampton's second win on the opening day of the season in the last 14 attempts
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.
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