- Marcus Tavernier (50')
Gary O'Neil's squad leapfrogged West Ham United into 14th place with 36 points from 33 games, seven points clear of the drop zone.
"We were in complete control," O'Neil told BT Sport. "Disappointed that we didn't put the game to bed because you knew that Southampton would get desperate towards the end and throw caution to the wind and then we had to show another side to us.
"But yeah, for the players to put on a performance like that in such a high-pressure game, really proud of them."
Southampton, who have won just six times this season and played for most of the night like a team destined for relegation, are six points adrift of the safety zone with only five games remaining.
Bournemouth dominated possession and were finally rewarded for their hard work in the 50th minute when Tavernier worked around a pair of Saints defenders before threading the ball, which took a slight deflection, into the far corner.
"A big three points for us and that's what we intended to do when we came into this game is to get all three points, because we know at the moment every point matters," said Tavernier.
"We've put in some good couple of performances in the past couple of weeks and this tops them off at the moment."
"It's starting to be harder and harder and then we just need to keep fighting and trying to perform every game and then to get a win," Selles said on the fight to avoid relegation.
"We have another game in three days and we need to recover quick. We show that we can perform against any team, (but) we showed today that we are not constant in that way, and we just need to be more constant and more robust in the things that we do."
Adam Armstrong had what was otherwise the Saints' best chance when Bournemouth failed to clear the ball out of the back in the 14th minute. But Armstrong's close-range shot clanged off the post.
Bournemouth briefly celebrated in the 18th minute when Dominic Solanke was played through one-on-one. Alex McCarthy made a terrific point-blank save before Vina followed it in to smash home the rebound. But the goal was disallowed for offside.
The torrential downpour at Southampton's Saint Mary's Stadium meant the players had to contend with a slippery pitch and at times they struggled to stay on their feet.
- Darren England
|Brighton & Hove Albion||6||5||0||1||+10||15|
|West Ham United||6||3||1||2||+1||10|