Marcus Tavernier scored the only goal of the game five minutes after the break to inflict more misery onto their South Coast rivals while boosting the Cherries' hopes of maintaining their top-flight status in the process.
The Saints thought they had snatched a point in the dying embers when substitute Che Adams fired beyond Neto from close range, but the striker's left boot was caught offside by VAR and Bournemouth eventually held on for maximum points.
Ruben Selles' side remain rooted to the foot of the table and sit six points adrift of safety with just five games remaining, while Gary O'Neil's men - who have now won three successive top-flight away games for the first time in their history - have climbed up to 14th place and sit seven points clear of the drop zone.
The most notable news before kickoff was a change in goal for Southampton, with shot-stopper Alex McCarthy handed his first Premier League start of the season at the expense of Gavin Bazunu.
On an extremely wet and stormy evening on the South Coast, both teams made a bright start to proceedings, particularly the Saints with Theo Walcott cutting inside from the right and firing the first shot on goal that had to be saved low down by Neto at his near post.
McCarthy's first involvement at the other end was a nervy one as he dawdled on the ball inside his own six-yard box and slipped before Dominic Solanke chased him down and blocked an attempted clearance.
The game became stretched early doors with both side looking to make their mark on the counter-attack. Walcott saw a header helped onto the top of the crossbar by Marcos Senesi shortly after a snapshot from Adam Armstrong from a tight angle was saved onto the post by the right boot of Neto.
Tavernier and Philip Billing both had chances at the other end moments later, before Bournemouth put the ball in the net on the 18-minute mark when Matias Vina fired a left-footed strike beyond McCarthy, who had previously made a good save to deny Solanke in a one-on-one. However, the goal was disallowed as Solanke was caught fractionally offside in the build-up.
After Solanke, who was a constant threat in the final third, came close with a fizzed effort over the bar following a mazy run into the box, Southampton were forced to make the first substitution of the evening after left-back Romain Perraud picked up an injury 10 minutes before the break.
Southampton lost their rhythm towards the end of the half and Bournemouth looked the most likely to break the deadlock, but the Saints managed to keep the scores level heading into the interval.
There were groans among the St Mary's faithful before the second half got underway when they discovered that top scorer and captain James Ward-Prowse would play no further part in the contest, allegedly due to illness, with centre-back Lyanco brought on as his replacement.
Bournemouth picked up from where they left off at the end of the first half and their persistence in the final third paid off as Tavernier opened the scoring on the 50-minute mark.
The Cherries attacker travelled into the box and cut inside from the right onto his favoured left foot before poking a deflected strike through a crowd of Saints defenders into the far corner.
Southampton looked to have ran out of ideas and had no focal point in attack to aim for, but that soon charged when Adams - who scored the only goal in the reverse fixture six months ago - came on at the expense of Walcott on the hour mark to partner Adam Armstrong in attack.
Bournemouth were dealt a blow heading into the final 15 minutes when Tavernier pulled up with an apparent hamstring injury after making a darting run down the right flank, with Adam Smith brought on as his replacement.
The Saints made slight improvements in the closing stages and they thought they had netted an equaliser in the 89th minute when Adams flicked an effort in off the crossbar after receiving a low cross from the right. However, VAR intervened and found that the striker's toe was in an offside position before receiving the ball inside the six-yard box.
Bournemouth played with a greater purpose throughout the contest, something that the Southampton supporters were craving to see from their side, but Selles and co ultimately lacked the cutting edge up top and the Cherries managed to comfortably see out the game to claim all three points.
Southampton will now prepare for a trick trip to St James' Park to face Champions League-chasing Newcastle United on Sunday, while Bournemouth play host to relegation-threatened Leeds United.