The Dutchman was teed up on the edge of the area by the excellent Dusan Tadic and connected with the outside of his boot to drive his shot into the top corner as Saints took the lead on 25 minutes.
The Baggies pressed for an equaliser but failed to score for the fifth time in their last six games.
They were continually thwarted by England goalkeeper Fraser Forster who made three stunning saves.
The first saw him claw away a Salomon Rondon header in the first half and he then denied Craig Dawson and Jonny Evans deep into injury time as Saints held on for the win.
Tony Pulis' side have now lost four of their last six and are stuttering in their attempts to achieve their best league finish since 1981, when they came fourth.
The win leaves ninth-placed Southampton just four points behind the Baggies, who stay eighth.
Scotland winger Matt Phillips made his first start since February, but he could not inspire West Brom.
Last season they failed to win any of their last nine league games, with five defeats and four draws.
They are three games into their final nine matches of this campaign and their record reads two defeats and one draw.
While goals are clearly a problem at the moment, the Albion defence is also struggling with just three clean sheets in their last 20 league games.
Albion were not short on chances with 17 shots in the game, six of which were on target. They had 18 attempts in the 2-0 midweek defeat by Watford and Pulis is disappointed his side are not taking their chances.
"We have had 35 shots over the last two games, we need to have more composure and steadiness in front of goal," Pulis told BBC Sport.
Still, barring a dramatic collapse, they should be able to achieve the Chinese owners' target of a top-10 finish this season.
Performances like today will put Forster back in contention to challenge Joe Hart for the England jersey.
The 29-year-old made six saves today and manager Claude Puel paid tribute. saying: "Fraser was the difference at the end, he preserved the three points."
It was his two injury-time saves that really caught the eye.
In the 93rd minute Jake Livermore played the ball over the top and Dawson managed to connect with a volley that Forster saved at point-blank range.
Two minutes later, Chris Brunt's corner was flicked on by Livermore and Evans' side-footed shot was slapped away by the former Newcastle keeper.
Before those heroics it had been Tadic who had starred for Saints. Since making his Premier League debut in August 2014, following his £10.9m move from FC Twente, he has provided 24 assists.
Only Chelsea's Cesc Fabregas (32), Arsenal's Mesut Ozil (30) and Tottenham's Christian Eriksen (26) have more.
Southampton have now lost just one of their last six league games, after losing six and winning just one of the seven before that.
Media playback is not supported on this device
Puel told BBC Sport: "It was an excellent performance. We played a good first-half and could have scored another goal. It was a perfect second half, you can see the character of the players and the team.
"To get a clean sheet here is good with the quality of West Brom and the quality of their set-pieces. After the win against Crystal Palace, it's another good performance in terms of consistency.
"Fraser was the difference at the end, he preserved the three points."
Media playback is not supported on this device
Pulis told BBC Sport: "We created better opportunities in the second half and as the game went on we controlled the last 25 minutes and I felt we did enough to get something out of the game.
"It is disappointing considering the chances were there, especially in the second half. We have had 35 shots over the last two games. We need to have more composure and steadiness in front of goal. But I can't fault my players today, over the last 25 minutes they showed their mettle and kept going."
Southampton welcome Manchester City to Saint Mary's on Saturday, while West Brom host Liverpool on Sunday.
Match ends, West Bromwich Albion 0, Southampton 1.
Second Half ends, West Bromwich Albion 0, Southampton 1.
Attempt saved. Jonny Evans (West Bromwich Albion) right footed shot from the centre of the box is saved in the top left corner. Assisted by Jake Livermore with a headed pass.
Corner,  West Bromwich Albion. Conceded by Jack Stephens.
Fraser Forster (Southampton) is shown the yellow card.
Attempt missed. Nyom (West Bromwich Albion) right footed shot from the centre of the box is too high.
Attempt saved. Craig Dawson (West Bromwich Albion) right footed shot from the centre of the box is saved in the bottom right corner. Assisted by Jake Livermore with a cross.
Foul by Pierre-Emile Højbjerg (Southampton).
Nacer Chadli (West Bromwich Albion) wins a free kick in the attacking half.
Pierre-Emile Højbjerg (Southampton) wins a free kick in the defensive half.
Foul by James McClean (West Bromwich Albion).
Corner,  West Bromwich Albion. Conceded by Ryan Bertrand.
Substitution, Southampton. Harrison Reed replaces Jordy Clasie.
Delay over. They are ready to continue.
Delay in match Pierre-Emile Højbjerg (Southampton) because of an injury.
Attempt blocked. Jake Livermore (West Bromwich Albion) right footed shot from outside the box is blocked. Assisted by Nyom.
Attempt blocked. Salomón Rondón (West Bromwich Albion) right footed shot from outside the box is blocked. Assisted by James Morrison.
Corner,  West Bromwich Albion. Conceded by Cédric Soares.
Foul by Shane Long (Southampton).
Craig Dawson (West Bromwich Albion) wins a free kick in the defensive half.
Attempt missed. Hal Robson-Kanu (West Bromwich Albion) right footed shot from the right side of the box is too high.
Cédric Soares (Southampton) wins a free kick in the defensive half.
Foul by Salomón Rondón (West Bromwich Albion).
Corner,  West Bromwich Albion. Conceded by Maya Yoshida.
Cédric Soares (Southampton) is shown the yellow card for a bad foul.
Foul by Cédric Soares (Southampton).
Nacer Chadli (West Bromwich Albion) wins a free kick in the defensive half.
Corner,  Southampton. Conceded by Chris Brunt.
Corner,  West Bromwich Albion. Conceded by Maya Yoshida.
Attempt blocked. Salomón Rondón (West Bromwich Albion) right footed shot from outside the box is blocked. Assisted by Nacer Chadli.
Foul by Shane Long (Southampton).
Jonny Evans (West Bromwich Albion) wins a free kick in the defensive half.
Shane Long (Southampton) wins a free kick on the left wing.
Foul by Craig Dawson (West Bromwich Albion).
Substitution, Southampton. Sam McQueen replaces James Ward-Prowse.
Substitution, Southampton. Josh Sims replaces Nathan Redmond.
Attempt missed. Dusan Tadic (Southampton) left footed shot from the right side of the box is close, but misses the top left corner.
Attempt saved. Nacer Chadli (West Bromwich Albion) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Hal Robson-Kanu.
Attempt saved. Salomón Rondón (West Bromwich Albion) header from the centre of the box is saved in the top left corner. Assisted by James McClean with a cross.
Attempt saved. Nathan Redmond (Southampton) right footed shot from the left side of the box is saved in the bottom left corner. Assisted by Cédric Soares with a cross.
Jordy Clasie's first-half strike proved the difference as Southampton beat West Brom to strengthen their grip on a top-10 finish.